Data Types
interface	besselj_series_cutoff

interface	besseljy_debye_cutoff

interface	besseljy_debye_fit

interface	bessely_series_cutoff

interface	hankel_debye_cutoff

interface	hankel_debye_fit

Functions/Subroutines
elemental real(real32) function	besseljy_debye_fit32 (x)

elemental logical function	besseljy_debye_cutoff32 (nu, x)

elemental real(real64) function	besseljy_debye_fit64 (x)

elemental logical function	besseljy_debye_cutoff64 (nu, x)

elemental real(real128) function	besseljy_debye_fit128 (x)

elemental logical function	besseljy_debye_cutoff128 (nu, x)

elemental logical function	besseljy_large_argument_cutoff (nu, x)

elemental logical function	hankel_debye_cutoff128 (nu, x)

elemental logical function	hankel_debye_cutoff64 (nu, x)

elemental real(real64) function	hankel_debye_fit64 (x)

elemental logical function	hankel_debye_cutoff32 (nu, x)

elemental real(real32) function	hankel_debye_fit32 (x)

elemental logical function	besselj_series_cutoff32 (x, nu)

elemental logical function	besselj_series_cutoff64 (x, nu)

elemental logical function	besselj_series_cutoff128 (x, nu)

elemental logical function	bessely_series_cutoff32 (nu, x)

elemental logical function	bessely_series_cutoff64 (nu, x)

elemental real(bk) function	besselj_power_series (nu, x)

elemental subroutine	bessely_power_series (nu, x, y, j)

pure real(bk) function, dimension(2)	besselj_down_recurrence (x, jnu, jnup1, nu_start, nu_end)

elemental subroutine	besselj_up_recurrence (x, jnu, jnum1, nu_start, nu_end, a, b)

elemental real(bk) function	cbrt (x)

pure real(bk) function	evalpoly (n, x, p)

pure real(bk) function	evalpoly8 (x, p)

pure real(bk) function	evalpoly7 (x, p)

pure real(bk) function	evalpoly5 (x, p)

pure real(bk) function	evalpoly4 (x, p)

pure real(bk) function	clenshaw_chebyshev (x, c)

elemental real(bk) function	muladd (a, x, y)

elemental logical function	isinteger (x)

Variables
integer, parameter	bk = real64

integer, parameter	bsize = int32

real(bk), parameter	zero = 0.00_BK

real(bk), parameter	one = 1.00_BK

real(bk), parameter	two = 2.00_BK

real(bk), parameter	three = 3.00_BK

real(bk), parameter	four = 4.00_BK

real(bk), parameter	five = 5.00_BK

real(bk), parameter	six = 6.00_BK

real(bk), parameter	half = 0.50_BK

real(bk), parameter	fourth = 0.25_BK

real(bk), parameter	twothd = 2.0_BK/3.0_BK

real(bk), parameter	third = 1.0_BK/3.0_BK

real(bk), parameter	sixth = 1.0_BK/6.0_BK

real(bk), parameter	pi = acos(-1.0_BK)

real(bk), parameter	oneosqpi = ONE/SQRT(PI)

real(bk), parameter	twoopi = TWO/PI

real(bk), parameter	pio2 = PI*HALF

real(bk), parameter	pio4 = PI*FOURTH

real(bk), parameter	sqpio2 = 1.253314137315500251207882642405522626503493370304969158314961788171146827303924_BK

real(bk), parameter	sq1o2pi = 0.3989422804014326779399460599343818684758586311649346576659258296706579258993008_BK

real(bk), parameter	sq2opi = 0.7978845608028653558798921198687637369517172623298693153318516593413158517986017_BK

real(bk), parameter	sq2o2 = 0.707106781186547524400844362104849039284835937688474036588339868995366239231051_BK

real(bk), parameter	thpio4 = 2.35619449019234492885_BK

real(bk), parameter	sq2pi = 2.5066282746310007_BK

real(bk), parameter	pipow3o2 = PI * sqrt(PI)

complex(bk), parameter	im = (ZERO, ONE)

real(bk), parameter	gamma_two_thirds = gamma(TWOTHD)

real(bk), parameter	gamma_one_third = gamma(THIRD)

real(bk), parameter	gamma_one_sixth = gamma(SIXTH)

real(bk), parameter	gamma_five_sixths = gamma(5.0_BK*SIXTH)

real(bk), dimension(2, 16), parameter	j0_roots = reshape([ 2.4048255576957730_BK, -1.1766916515308940e-16_BK, 3.8317059702075125_BK, -1.5269184090088067e-16_BK, 5.5200781102863110_BK, +8.0885971461467220e-17_BK, 7.0155866698156190_BK, -9.4141656534103890e-17_BK, 8.6537279129110130_BK, -2.9281260732077900e-16_BK, 10.173468135062722_BK, +4.4821622747688880e-16_BK, 11.791534439014281_BK, +2.8129569127787350e-16_BK, 13.323691936314223_BK, +2.6004080647188130e-16_BK, 14.930917708487787_BK, -7.0705145059830740e-16_BK, 16.470630050877634_BK, -1.6190195447981280e-15_BK, 18.071063967910924_BK, -9.6580480894262090e-16_BK, 19.615858510468243_BK, -1.0044456345266160e-15_BK, 21.211636629879260_BK, +4.9470774287840680e-16_BK, 22.760084380592772_BK, -4.9257493736149220e-16_BK, 24.352471530749302_BK, +9.1690671339510660e-16_BK, 25.903672087618382_BK, +4.8945307264198250e-16_BK], [2,16])

real(bk), dimension(2, 16), parameter	j1_roots = reshape([ 1.8411837813406593_BK, +4.7898393919093694e-18_BK, 3.8317059702075125_BK, -1.5269184090088067e-16_BK, 5.3314427735250325_BK, +1.5109105349471405e-16_BK, 7.0155866698156190_BK, -9.4141656534103890e-17_BK, 8.5363163663462860_BK, -1.5433871213307537e-16_BK, 10.173468135062722_BK, +4.4821622747688880e-16_BK, 11.706004902592063_BK, +7.1213669422982460e-16_BK, 13.323691936314223_BK, +2.6004080647188130e-16_BK, 14.863588633909034_BK, -6.2657889887818790e-16_BK, 16.470630050877634_BK, -1.6190195447981280e-15_BK, 18.015527862681804_BK, -1.1196999448424267e-16_BK, 19.615858510468243_BK, -1.0044456345266160e-15_BK, 21.164369859188790_BK, +1.7024131380423588e-15_BK, 22.760084380592772_BK, -4.9257493736149220e-16_BK, 24.311326857210776_BK, -2.6147985585371720e-16_BK, 25.903672087618382_BK, +4.8945307264198250e-16_BK], [2,16])

real(bk), dimension(*), parameter	j0_poly_pio2 = [ +1.00000000000000000000_BK , -0.25000000000000000000_BK , +0.01562499999999994000_BK , -0.00043402777777725544_BK , +6.781684026082576000000e-6_BK , -6.781683757550061e-8_BK , 4.709479394601058e-10_BK , -2.4016837144506874e-12_BK , 9.104258208703104e-15_BK ]

real(bk), dimension(*), parameter	j1_poly_pio2 = [ 0.5_BK , -0.0624999999999989_BK , 0.002604166666657291_BK , -5.42534721917933e-5_BK , 6.781683542660179e-7_BK , -5.651361336587487e-9_BK , 3.36191211106159e-11_BK , -1.4511302591871352e-13_BK ]

real(bk), dimension(14, 16), parameter	j0_polys = reshape([ 0.0000000000000000000_BK, -0.5191474972894669_BK, 0.10793870175491979_BK, 0.05660177443794914_BK, -0.008657669593292222_BK, -0.0021942003590739974_BK, 0.0002643770365942964_BK, 4.37291931443113e-5_BK, -4.338825419759815e-6_BK, -5.304927679598406e-7_BK, 4.469819175606667e-8_BK, 4.3284827345621115e-9_BK, -3.135111000732148e-10_BK, -2.628876489517534e-11_BK, -0.402759395702553_BK, 2.476919088072758e-16_BK, 0.20137969785127532_BK, -0.017518715285670765_BK, -0.013352611033152278_BK, 0.0010359438492839443_BK, 0.00037218755624680334_BK,-2.4952042421113972e-5_BK, -5.776086353844158e-6_BK, 3.374317129436161e-7_BK, 5.727482259215452e-8_BK, -2.9561880489355444e-9_BK, -3.905845672635605e-10_BK, 1.971332566705736e-11_BK, 0.000000000000000000_BK, 0.34026480655836816_BK, -0.030820651425593214_BK, -0.05298855286760721_BK, 0.004631042145890388_BK, 0.002257440229081131_BK, -0.00017518572879518415_BK,-4.6521091062878115e-5_BK, 3.199785909661533e-6_BK, 5.716500268232186e-7_BK, -3.5112898510841466e-8_BK, -4.684643389757727e-9_BK, 2.562685034682206e-10_BK, 2.7958958795750104e-11_BK, 0.30011575252613254_BK, -1.6640272822046001e-16_BK,-0.15005787626306408_BK, 0.007129737603121546_BK, 0.011742619737383848_BK, -0.0006260583453094324_BK, -0.00035093119008693753_BK, 1.7929701912295164e-5_BK, 5.6239324892485754e-6_BK, -2.668437501970219e-7_BK, -5.6648488273749086e-8_BK, 2.48117399780498e-9_BK, 3.8876537586241154e-10_BK,-1.6657136713437192e-11_BK, 0.000000000000000000_BK, -0.27145229992838193_BK, 0.015684124960953488_BK, 0.044033774963413_BK, -0.0025093022271948434_BK, -0.0020603351551475315_BK, 0.00011243486771159352_BK, 4.482303558813413e-5_BK, -2.288390108003442e-6_BK, -5.679383588459768e-7_BK, 2.693939234375692e-8_BK, 4.737285529934781e-9_BK, -2.0612709555352797e-10_BK,-2.8163166483726606e-11_BK, -0.2497048770578432_BK, 1.1807897766765572e-16_BK, 0.12485243852891914_BK, -0.0040907858517059345_BK, -0.010102792347641438_BK, 0.00038536375952213334_BK, 0.00031859711440332953_BK,-1.2373899600646271e-5_BK, -5.3013932979548665e-6_BK, 2.001098153528186e-7_BK, 5.4711629662471434e-8_BK, -1.9724572531751518e-9_BK, -3.8121398193699247e-10_BK, 1.3667679743782715e-11_BK, 0.000000000000000000_BK, 0.23245983136472478_BK, -0.009857064513825458_BK, -0.03818600911162367_BK, 0.0016073972920762946_BK, 0.0018420433388794816_BK, -7.581358465623415e-5_BK, -4.159284549011371e-5_BK, 1.650645590334915e-6_BK, 5.425453494592871e-7_BK, -2.0556207467977526e-8_BK, -4.620018928884712e-9_BK, 1.642028058414746e-10_BK, 2.7701605444102412e-11_BK, 0.21835940724787295_BK, -8.89726402965429e-17_BK, -0.10917970362393398_BK, 0.0027314677279632535_BK, 0.008944552393700088_BK, -0.00026391472261453583_BK, -0.00028847875053074687_BK, 8.858193371737123e-6_BK, 4.9233776180403375e-6_BK, -1.5077786827161215e-7_BK, -5.190218733666561e-8_BK, 1.5539413886301204e-9_BK, 3.674809363354973e-10_BK, -1.1113645791216594e-11_BK, 0.00000000000000000_BK, -0.20654643307799603_BK, 0.006916736034268416_BK, 0.034115572697347704_BK, -0.001137276252948717_BK, -0.0016680057255530109_BK, 5.4841792064182565e-5_BK, 3.837965853474541e-5_BK, -1.2335804050962046e-6_BK, -5.106259295634553e-7_BK, 1.592333632709497e-8_BK, 4.423517565793139e-9_BK, -1.3138837384184105e-10_BK,-2.6809397212536384e-11_BK, -0.19646537146865717_BK, 6.979167865106427e-17_BK, 0.09823268573432613_BK, -0.001988037402152532_BK, -0.008095530671166083_BK, 0.00019440675128712672_BK, 0.0002640383898036336_BK, -6.666777683303928e-6_BK, -4.5715696772304925e-6_BK, 1.1666296153560847e-7_BK, 4.8913639696764225e-8_BK, -1.2379867207945651e-9_BK, -3.508930968415813e-10_BK, 9.07632091591013e-12_BK, 0.00000000000000000_BK, 0.18772880304043943_BK, -0.005194182350684612_BK, -0.031096513233785917_BK, 0.0008577442641273341_BK, 0.0015312251534677639_BK, -4.184307585284775e-5_BK, -3.5603170534217916e-5_BK, 9.58002109234601e-7_BK, 4.795250964600283e-7_BK, -1.263434500625308e-8_BK, -4.20550167685701e-9_BK, 1.065791122326672e-10_BK, 2.5727417675684577e-11_BK, 0.18006337534431555_BK, -5.638484737644332e-17_BK, -0.09003168767215539_BK, 0.0015299132863046024_BK, 0.0074441453680234426_BK, -0.00015060569680378768_BK, -0.0002443398416353605_BK, 5.227001519013193e-6_BK, 4.267152607972633e-6_BK, -9.295966007495808e-8_BK, -4.610438011417262e-8_BK, 1.0049092632275165e-9_BK, 3.339442682325105e-10_BK, -7.4991079301099e-12_BK, 0.00000000000000000_BK, -0.17326589422922986_BK, 0.004084217951979124_BK, 0.028749284970146657_BK, -0.0006761643016121907_BK, -0.0014215899173758441_BK, 3.320978125391802e-5_BK, 3.3264379323815026e-5_BK, -7.684444100376941e-7_BK, -4.515479818833484e-7_BK, 1.0271599456634145e-8_BK, 3.993903280527723e-9_BK, -8.793975528824604e-11_BK, -2.4610374225652004e-11_BK, -0.16718460047381803_BK, 4.662597138876655e-17_BK, 0.08359230023690671_BK, -0.0012242529339116864_BK, -0.006925682915280748_BK, 0.00012100729852042988_BK, 0.00022821854128498174_BK,-4.230799709959437e-6_BK, -4.007618360337058e-6_BK, 7.601217108010105e-8_BK, 4.358483157250522e-8_BK, -8.317621452517008e-10_BK, -3.178805429572483e-10_BK, 6.284538399593043e-12_BK, 0.000000000000000000_BK, 0.16170155068925002_BK, -0.0033200234006036146_BK, -0.02685937038656159_BK, 0.0005505380905909195_BK, 0.0013316994659124243_BK, -2.715683205388875e-5_BK, -3.1289544794362e-5_BK, 6.326900360777323e-7_BK, 4.2697141781883964e-7_BK, -8.532447325590315e-9_BK, -3.799009445641295e-9_BK, 7.379552811590934e-11_BK, 2.353654960834717e-11_BK, 0.15672498625285222_BK, 1.1464880342445208e-19_BK,-0.07836249312642612_BK, 0.0010083833270351796_BK, 0.006501011610557426_BK, -9.993664895655577e-5_BK, -0.00021478298462967253_BK, 3.511086890959515e-6_BK, 3.7857022791122945e-6_BK, -6.350944888510364e-8_BK, -4.135588012575766e-8_BK, 7.135988717747828e-10_BK, 3.2075281131621564e-10_BK, 2.208506585533542e-12_BK], [14,16])

real(bk), dimension(14, 16), parameter	j1_polys = reshape([ 0.5818652242815964_BK, 8.973834293036876e-17_BK, -0.20511071214777496_BK, 0.006058948324597746_BK, 0.013801769808047723_BK, -0.0003723170971916689_BK, -0.0003949590750416506_BK, 9.202953658715798e-6_BK, 6.267292697927347e-6_BK, -1.2681571675674473e-7_BK, -6.319326736018798e-8_BK, 1.057852721352679e-9_BK, 4.839653511789343e-10_BK, -2.1534683937074676e-11_BK, 0.0000000000000000000_BK, -0.402759395702553_BK, 0.05255614585697725_BK, 0.053410444132722765_BK, -0.005179719245639115_BK, -0.00223312533910116_BK, 0.00017466429071755533_BK, 4.6208700909637e-5_BK, -3.0368632747366735e-6_BK, -5.727790851165856e-7_BK, 3.248220586398651e-8_BK, 4.732693354840469e-9_BK, -2.346792988667587e-10_BK, -2.607612190048509e-11_BK, -0.34612620185379156_BK, 2.6002760076991505e-17_BK, 0.16697453550109428_BK, -0.009678268542879972_BK, -0.012099225779175138_BK, 0.0006654009006841076_BK, 0.0003541389011182841_BK, -1.742720356958137e-5_BK, -5.655294960447268e-6_BK, 2.484316221112215e-7_BK, 5.7101369594782676e-8_BK, -2.2587104440771904e-9_BK, -3.9854619701676605e-10_BK, 1.854508641982197e-11_BK, 0.00000000000000000000_BK, 0.30011575252613254_BK, -0.02138921280934146_BK, -0.04697047894974007_BK, 0.0031302917260424344_BK, 0.0021055871432169443_BK, -0.00012550790947431806_BK,-4.499147505171648e-5_BK, 2.401580334889493e-6_BK, 5.665260872870135e-7_BK, -2.7272058756924113e-8_BK, -4.718921752439826e-9_BK, 2.045523137027535e-10_BK, 2.6923755198436e-11_BK, 0.27329994163319987_BK, -1.3511933704624036e-16_BK,-0.13477468037992396_BK, 0.005116340346495344_BK, 0.010631861751990702_BK, -0.000448743683849691_BK, -0.0003268000185531749_BK, 1.3382556752353113e-5_BK, 5.363177082527157e-6_BK, -2.0647461181851255e-7_BK, -5.499892476485602e-8_BK, 1.9780335410646812e-9_BK, 3.8456897851545063e-10_BK,-1.5543946040865833e-11_BK, 0.0000000000000000000_BK, -0.2497048770578432_BK, 0.012272357555101388_BK, 0.04041116939079181_BK, -0.0019268187972545589_BK, -0.0019115826893618788_BK, 8.661729445925766e-5_BK, 4.241116264477775e-5_BK, -1.800978985430059e-6_BK, -5.47159694982648e-7_BK, 2.1682608288127194e-8_BK, 4.629875997238198e-9_BK, -1.6946465290961774e-10_BK,-2.7001263147077087e-11_BK, -0.23330441717143408_BK, 1.3347222236161232e-16_BK, 0.11580092244607755_BK, -0.0032489977328297747_BK, -0.009372527206041913_BK, 0.0003036138212749204_BK, 0.00029804555521007126_BK,-9.813819271763006e-6_BK, -5.0242293237237345e-6_BK, 1.6136482548346424e-7_BK, 5.251755806094281e-8_BK, -1.6213723779041528e-9_BK, -3.7130918416720704e-10_BK, 1.2840797195120732e-11_BK, 0.00000000000000000000_BK, 0.21835940724787295_BK, -0.008194403183877394_BK, -0.03577820957502993_BK, 0.001319573612804675_BK, 0.0017308725061602815_BK, -6.200735153951766e-5_BK, -3.938703730297954e-5_BK, 1.3569938030086903e-6_BK, 5.190652330962483e-7_BK, -1.7082573736581586e-8_BK, -4.464580500726025e-9_BK, 1.3835552663370753e-10_BK, 2.6508049073606443e-11_BK, 0.20701265272531905_BK, -1.1572365385200866e-16_BK,-0.10303781563402706_BK, 0.002289729546293356_BK, 0.008432435058846974_BK, -0.00021965941971569214_BK, -0.000272721543802475_BK, 7.36909520166486e-6_BK, 4.682127415369e-6_BK, -1.2611406291992532e-7_BK, -4.9733737497256667e-8_BK, 1.313333637862963e-9_BK, 3.5584811981981077e-10_BK,-1.0581432980865016e-11_BK, 0.00000000000000000000_BK,-0.19646537146865717_BK, 0.005964112206447895_BK, 0.032382122684890324_BK, -0.0009720337562254532_BK, -0.0015842303417456071_BK, 4.6667442166602986e-5_BK, 3.6572573450276185e-5_BK, -1.0499611641790313e-6_BK, -4.891787571238003e-7_BK, 1.3609422867092438e-8_BK, 4.2640592578446675e-9_BK, -1.1321195999108497e-10_BK,-2.5685037344174917e-11_BK, -0.18801748852581776_BK, 9.806595982257605e-17_BK, 0.09371909377243136_BK, -0.0017233243363111925_BK, -0.007714266760106843_BK, 0.00016755862384546863_BK, 0.000251827174474777_BK, -5.7335177376628445e-6_BK, -4.372425030172481e-6_BK, 1.0045839852031556e-7_BK, 4.698184959516747e-8_BK, -1.0717704296017814e-9_BK, -3.3952344362582674e-10_BK, 8.773851724781324e-12_BK, 0.00000000000000000000_BK, 0.18006337534431555_BK, -0.004589739858905968_BK, -0.029776581472313136_BK, 0.0007530284838491313_BK, 0.0014660390526475475_BK, -3.658900932751018e-5_BK, -3.4137236390211275e-5_BK, 8.366325091910564e-7_BK, 4.6108475352995054e-7_BK, -1.1047200388967438e-8_BK, -4.058793425595929e-9_BK, 9.363513647344476e-11_BK, 2.4720051360744732e-11_BK, 0.1734590492857464_BK, -8.319859584484218e-17_BK, -0.08653590193876039_BK, 0.0013568189856187354_BK, 0.007147216520714834_BK, -0.00013295776598760658_BK, -0.00023462959289705953_BK, 4.6031437800947915e-6_BK, 4.103196271673978e-6_BK, -8.18373301294018e-8_BK, -4.44403211204062e-8_BK, 8.872617322304839e-10_BK, 3.2359730989751983e-10_BK,-7.354373969368619e-12_BK, 0.00000000000000000000_BK,-0.16718460047381806_BK, 0.0036727588017285762_BK, 0.02770273166133465_BK, -0.0006050364924617241_BK, -0.0013693112504440895_BK, 2.9615596890234806e-5_BK, 3.206096184277923e-5_BK, -6.841058767433935e-7_BK, -4.358877331737043e-7_BK, 9.143763763164119e-9_BK, 3.864037532317281e-9_BK, -7.851667555762691e-11_BK, -2.3728757802646805e-11_BK, -0.1618382095526585_BK, 7.115722920799028e-17_BK, 0.08078219522574913_BK, -0.0011038527651152986_BK, -0.006686444726790514_BK, 0.00010870535083026479_BK, 0.00022030197347228358_BK,-3.791805814546456e-6_BK, -3.871147931227952e-6_BK, 6.80607764766372e-8_BK, 4.2160129307780366e-8_BK, -7.460427055677985e-10_BK, -3.0872139357605097e-10_BK, 6.24158293622982e-12_BK, 0.00000000000000000000_BK, 0.15672498625285222_BK, -0.0030251499811055965_BK, -0.026004046442225856_BK, 0.0004996832448037306_BK, 0.001288697907658241_BK, -2.457760943647847e-5_BK, -3.02856199504406e-5_BK, 5.715983781675481e-7_BK, 4.136275513873783e-7_BK, -7.703846567878601e-9_BK, -3.6853569596797437e-9_BK, 6.676439988396374e-11_BK, 2.277101500922319e-11_BK], [14,16])

real(bk), dimension(29, 17), parameter	bessely_cheb_weights = reshape([ -0.030017698430846347_BK, 0.04841599615543705_BK, -0.06170112748210926_BK, 0.010992867154582408_BK, -0.03732304718455494_BK, -0.06704282983696781_BK, 0.05527054188949959_BK, 0.023931299324571078_BK, -0.01660982874247215_BK, -0.0038257184915278875_BK, 0.0024486563159734553_BK, 0.00036760669126412974_BK, -0.00022289024621774598_BK, -2.400043085835714e-5_BK, 1.3967165370379739e-5_BK, 1.1481395619070928e-6_BK, -6.449732666954525e-7_BK, -4.1980803435719734e-8_BK, 2.2894937763100794e-8_BK, 1.228873366161081e-9_BK, -6.497632451926297e-10_BK, -2.8492149116234243e-11_BK, 1.4818408405099196e-11_BK, 6.100556567848311e-13_BK, -2.9867774919978274e-13_BK, -6.185528280054444e-15_BK, 3.7311423791866865e-15_BK, 4.123685520036296e-16_BK, -1.3481279584734043e-16_BK, 0.04160742192322324_BK, 0.034668235600932615_BK, 0.11174468340078995_BK, -0.04099618095057443_BK, 0.1254503646682523_BK, -0.13898784797365799_BK, -0.09733131946545694_BK, 0.07149834579877713_BK, 0.023375835755720973_BK, -0.014572641168112577_BK, -0.002981779009597293_BK, 0.0016841968136507765_BK, 0.0002422436246301404_BK, -0.000127737004832643_BK, -1.3814377122225202e-5_BK, 6.9111332786206e-6_BK, 5.866764647818481e-7_BK, -2.8135569182003675e-7_BK, -1.9403344167501224e-8_BK, 8.972400084810467e-9_BK, 5.113342130666102e-10_BK, -2.2951010536509386e-10_BK, -1.1304711135449809e-11_BK, 4.905817815473565e-12_BK, 1.894873147278986e-13_BK, -8.217632923341561e-14_BK, -4.218847493575595e-15_BK, 1.6772297836301473e-15_BK, -7.137148015447435e-17_BK, 0.022713476918759194_BK, -0.03501714644493984_BK, 0.04900399934159489_BK, -0.004572920361822816_BK, 0.03414506477673644_BK, 0.0583364038403724_BK, -0.04624123224424829_BK, -0.02357706101501925_BK, 0.01424650161095809_BK, 0.004131847507694573_BK, -0.0021768978247202514_BK, -0.0004222406947531938_BK, 0.00020419469487529897_BK, 2.882041410641021e-5_BK, -1.3118879606205788e-5_BK, -1.419547866831786e-6_BK, 6.171197932015276e-7_BK, 5.3215526542899864e-8_BK, -2.2283397359466684e-8_BK, -1.5689346295358737e-9_BK, 6.370162334131838e-10_BK, 3.785641839686755e-11_BK, -1.4927226121841386e-11_BK, -7.280852508197353e-13_BK, 2.822365357297534e-13_BK, 1.4096858601066386e-14_BK, -5.194257722353411e-15_BK, -1.784287003861859e-17_BK, 1.784287003861859e-17_BK, -0.005482743163667869_BK, -0.0026156864489958096_BK, -0.013446106107341984_BK, 0.003959772572751581_BK, -0.013050739904566335_BK, 0.012785648905104951_BK, 0.012302789524159771_BK, -0.007125881422379595_BK, -0.0032178006311644504_BK, 0.0015436443743600617_BK, 0.0004291283948110706_BK, -0.00018601906106350898_BK, -3.5730026469563336e-5_BK, 1.4521000123576475e-5_BK, 2.0641877773886624e-6_BK, -8.0134383976041e-7_BK, -8.833134689166324e-8_BK, 3.3105750509021536e-8_BK, 2.9248427531622776e-9_BK, -1.0652720751644758e-9_BK, -7.761774457286969e-11_BK, 2.758318276166857e-11_BK, 1.6716350526024826e-12_BK, -5.818832518996889e-13_BK, -3.163144349623995e-14_BK, 1.0744381574921492e-14_BK, 3.598312124454748e-16_BK, -1.2688263138573217e-16_BK, -1.4373423086664974e-17_BK, -0.000821102524680051_BK, 0.001369166415512963_BK, -0.0017176445978307614_BK, -0.00038167202153855176_BK, -0.0010693704116036165_BK, -0.0034162564467415902_BK, 0.0019105668931819009_BK, 0.0015608651654028757_BK, -0.000662690872417737_BK, -0.00028896692147194577_BK, 0.00010910809251752316_BK, 3.0258725355010946e-5_BK, -1.0717669999955374e-5_BK, -2.0862028639579696e-6_BK, 7.091627814767861e-7_BK, 1.0306000805131983e-7_BK, -3.4017752731151496e-8_BK, -3.856023535105163e-9_BK, 1.2437339960318393e-9_BK, 1.1358064900927889e-10_BK, -3.594555586962962e-11_BK, -2.7016821319796643e-12_BK, 8.405911755350802e-13_BK, 5.4115690103654197e-14_BK, -1.660105584745862e-14_BK, -8.187894806610529e-16_BK, 2.462687791788503e-16_BK, 2.0816681711721685e-17_BK, -6.443258625056712e-18_BK, 0.0002240588217758784_BK, -2.139628782819116e-5_BK, 0.0004963922147532327_BK, -0.00011956525731319659_BK, 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6.146714709097454e-8_BK, -1.4757833806872662e-8_BK, -3.0347995540046756e-9_BK, 7.310991241996968e-10_BK, 1.1291045426976899e-10_BK, -2.724231275323183e-11_BK, -3.306873481836321e-12_BK, 7.984081946667783e-13_BK, 7.777996686699921e-14_BK, -1.874952442498305e-14_BK, -1.5555232495803793e-15_BK, 3.750913580232083e-16_BK, 2.4244503044553087e-17_BK, -6.63977026881971e-18_BK, -8.441288342922856e-19_BK, 3.7947076036992655e-19_BK, -3.837876843131191e-6_BK, 1.5306249581045373e-6_BK, -7.808225833446716e-6_BK, 8.447928863780004e-7_BK, -4.570697567070479e-6_BK, -4.1982552639485557e-7_BK, 8.226238919809268e-6_BK, -9.86994172463081e-7_BK, -2.6319604894434756e-6_BK, 4.2742958932228587e-7_BK, 3.841104494715522e-7_BK, -7.011130365317191e-8_BK, -3.295984466784781e-8_BK, 6.37554898520718e-9_BK, 1.9212842748116095e-9_BK, -3.851870296260733e-10_BK, -8.157917257527438e-11_BK, 1.6727904537992146e-11_BK, 2.682049173124509e-12_BK, -5.589600448593574e-13_BK, -6.949400331178381e-14_BK, 1.4635958089930247e-14_BK, 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-8.524800253702236e-9_BK, 5.163074759458915e-8_BK, 1.7587774571193398e-8_BK, 1.5532689836449176e-8_BK, 4.569379005731088e-8_BK, -7.364565287663236e-8_BK, -1.3794427678087878e-8_BK, 2.8705869772299055e-8_BK, -2.180238319299374e-10_BK, -4.6124233142017096e-9_BK, 3.6839126250828555e-10_BK, 4.0853238049027397e-10_BK, -4.58540375117209e-11_BK, -2.4105895138400274e-11_BK, 3.1690572156845862e-12_BK, 1.025021315725097e-12_BK, -1.4748687505667043e-13_BK, -3.336472532024983e-14_BK, 5.062095043025821e-15_BK, 8.815484952439681e-16_BK, -1.390034081631452e-16_BK, -1.9199758208465145e-17_BK, 2.8599694051079214e-18_BK, 4.412739143428028e-19_BK, -1.4432387356775567e-18_BK, -2.3578466668818103e-18_BK, -8.403587813975867e-19_BK, -2.0135183203302226e-19_BK, -2.7963515253359716e-9_BK, 2.6599405451754447e-9_BK, -5.363225685883765e-9_BK, 3.919112883175106e-9_BK, -2.6445728931356353e-9_BK, 3.986389181091895e-9_BK, 4.369788563535614e-9_BK, -4.202468942903132e-9_BK, -8.620553821731379e-10_BK, 1.1190715605385904e-9_BK, 1.6458619897562414e-11_BK, -1.364556955782257e-10_BK, 7.770660894600997e-12_BK, 9.797565423719047e-12_BK, -8.709272762295716e-13_BK, -4.951317701122077e-13_BK, 5.5017193500686674e-14_BK, 1.7973668773098524e-14_BK, -2.186053134804191e-15_BK, -5.417976610912264e-16_BK, 7.265668497060572e-17_BK, 1.0657145676262853e-17_BK, -1.4951583811856726e-18_BK, 1.001165055851074e-19_BK, -4.215593642978497e-19_BK, -8.996650316071422e-19_BK, 1.1892060156355519e-18_BK, -5.459522028374813e-19_BK, -9.29316147844718e-19_BK, -2.869285397772589e-11_BK, -1.425452662669203e-10_BK, -1.4765859863811186e-11_BK, -3.584266980792905e-10_BK, 1.2630165211284162e-10_BK, -4.813898813698495e-10_BK, 2.9823341363420924e-10_BK, 2.736833504070133e-10_BK, -1.789940159530945e-10_BK, -3.709803166716433e-11_BK, 3.4844491459805023e-11_BK, 8.72681373200755e-13_BK, -3.2915591662608672e-12_BK, 1.3002232883748757e-13_BK, 1.9753949839973547e-13_BK, -1.4075604115824882e-14_BK, -8.601511614454014e-15_BK, 8.194975088384275e-16_BK, 2.6866096515073e-16_BK, -2.6539953077529138e-17_BK, -6.38116169641218e-18_BK, -1.8536358293679684e-18_BK, 4.749772369976817e-19_BK, -6.718043393812506e-19_BK, 1.608438964002761e-19_BK, 5.165497356149306e-20_BK, 2.605394963005647e-19_BK, 1.0581028516295723e-19_BK, 3.601100072898283e-19_BK, 1.7263987678277334e-11_BK, -1.3813366927208365e-11_BK, 2.934247457063122e-11_BK, -7.979165795689896e-12_BK, 4.195660738851445e-12_BK, 3.4756966192072763e-12_BK, -3.8868044414248185e-11_BK, 1.4360156231687025e-11_BK, 1.2343845937660092e-11_BK, -6.048594850472885e-12_BK, -1.1764419064241353e-12_BK, 8.840620586141411e-13_BK, 2.5310500957954275e-14_BK, -6.57823088425572e-14_BK, 1.5812120648028614e-15_BK, 3.437403053731452e-15_BK, -2.0773399722137888e-16_BK, -1.2502298901942747e-16_BK, 1.1188335458126739e-17_BK, 1.318770475529763e-18_BK, 1.826317128659254e-18_BK, -1.371135591032674e-18_BK, -7.556266590585322e-19_BK, -1.3319774595248458e-19_BK, -6.907940207156658e-20_BK, 1.774511101624311e-18_BK, -4.537139020388408e-20_BK, 4.949220345202049e-19_BK, -1.1868141638100254e-18_BK, -8.498193197325338e-13_BK, 1.953201750327066e-12_BK, -1.6836406424518253e-12_BK, 2.5267159459094905e-12_BK, -1.1786713409725903e-12_BK, 2.057320315641163e-12_BK, 2.5591575645466365e-13_BK, -2.0678475108903006e-12_BK, 5.290174964157149e-13_BK, 4.2270269001999225e-13_BK, -1.680245826111033e-13_BK, -2.838265511092047e-14_BK, 1.8427577852297096e-14_BK, 5.755842428415847e-16_BK, -1.1124766162836294e-15_BK, 1.08483878138819e-17_BK, 5.233365672134661e-17_BK, -4.1398608828316095e-18_BK, -1.5252680555707005e-18_BK, 1.5518391236648752e-21_BK, -1.914160606977295e-18_BK, -1.1560851262788287e-18_BK, 8.614032803477796e-19_BK, -2.4613082189127555e-18_BK, 2.3715585034500812e-18_BK, -7.375149035246488e-19_BK, 1.5108762141152207e-18_BK, -1.5506658311469656e-18_BK, 8.17023779980148e-19_BK, -2.5827236864549892e-14_BK, -3.4718790561504414e-14_BK, -2.2011098530056326e-14_BK, -9.110104031477491e-14_BK, 7.290507373316453e-14_BK, -1.234623611877002e-13_BK, 1.6275850841628636e-13_BK, 1.798444625683851e-14_BK, -8.154482889879963e-14_BK, 1.634453336575052e-14_BK, 1.129456516347965e-14_BK, -3.897439775077071e-15_BK, -5.305238116730616e-16_BK, 3.1481637373066765e-16_BK, 1.2762608430395386e-17_BK, -1.6640493419786607e-17_BK, 4.907490184278107e-19_BK, 3.285996490596493e-19_BK, -1.6693969668826682e-18_BK, -6.276996493483055e-19_BK, 2.2721860225308528e-18_BK, -1.0636166658032876e-18_BK, 5.4043840077706323e-20_BK, -6.733003923003965e-19_BK, 8.654687466171472e-19_BK, -1.6353891516146702e-18_BK, -1.1401886941945345e-18_BK, 1.806451000706121e-18_BK, 1.0454806663253078e-18_BK, 4.9388506677207545e-15_BK, -8.11264980108463e-15_BK, 8.15564695267678e-15_BK, -6.6179014247901285e-15_BK, 1.2560443562777774e-15_BK, -1.1626485837362674e-15_BK, -8.428647433288211e-15_BK, 8.040878625052107e-15_BK, 7.604076442794149e-16_BK, -2.509940602859596e-15_BK, 4.433411320740124e-16_BK, 2.4051574424535735e-16_BK, -7.97263854654364e-17_BK, -8.468775456115063e-18_BK, 3.0977204928150507e-18_BK, -2.763609694292828e-18_BK, -4.528057493615123e-18_BK, 8.090667992714159e-18_BK, -5.7670273029389466e-18_BK, 6.935237082901993e-18_BK, 2.3956539089710175e-18_BK, 3.5297683311975285e-18_BK, -2.6680862870119677e-19_BK, -1.124331067925833e-18_BK, -3.969891564639305e-18_BK, 3.4988194829519685e-18_BK, 8.636411459915624e-19_BK, -1.3895984430563314e-18_BK, 1.7657006809049643e-18_BK, -2.058125495426769e-16_BK, 6.08114692374987e-16_BK, -4.430737266654462e-16_BK, 7.070791826861885e-16_BK, -4.496672312473068e-16_BK, 4.992680927678948e-16_BK, -2.0005398723221536e-16_BK, -4.085152288266179e-16_BK, 2.963046065367326e-16_BK, 1.9081397648228198e-17_BK, -6.065778883208153e-17_BK, 1.2267254817829564e-17_BK, 2.5241246780253446e-18_BK, 5.364001077188067e-19_BK, -1.1151793774136653e-18_BK, -2.647497194530543e-19_BK, -9.99558548618923e-19_BK, 1.9545043306813755e-18_BK, 1.0295729550672243e-18_BK, 5.850363951633064e-19_BK, 2.039938658283451e-19_BK, -1.622964422184252e-18_BK, -2.1240860691038883e-18_BK, 2.0835979355758296e-18_BK, -1.5423943263121515e-19_BK, -5.576729517866199e-19_BK, -3.7259501367076117e-20_BK, -1.8905808347578018e-19_BK, -1.4869058365515489e-18_BK], [29,17])

real(bk), dimension(8), parameter	yp_y0 = [-1.84950800436986690637E16_BK, 4.42733268572569800351E16_BK, -3.46628303384729719441E15_BK, 8.75906394395366999549E13_BK, -9.82136065717911466409E11_BK, 5.43526477051876500413E9_BK, -1.46639295903971606143E07_BK, 1.55924367855235737965E4_BK]

real(bk), dimension(8), parameter	yq_y0 = [2.50596256172653059228E17_BK, 3.17157752842975028269E15_BK, 2.02979612750105546709E13_BK, 8.64002487103935000337E10_BK, 2.68919633393814121987E08_BK, 6.26107330137134956842E05_BK, 1.04128353664259848412E03_BK, 1.00000000000000000000E00_BK]

real(bk), dimension(7), parameter	pp_y0 = [9.99999999999999997821E-1_BK, 5.30324038235394892183E00_BK, 8.74716500199817011941E00_BK, 5.44725003058768775090E00_BK, 1.23953371646414299388E00_BK, 8.28352392107440799803E-2_BK, 7.96936729297347051624E-4_BK]

real(bk), dimension(7), parameter	pq_y0 = [1.00000000000000000218E00_BK, 5.30605288235394617618E00_BK, 8.76190883237069594232E00_BK, 5.47097740330417105182E00_BK, 1.25352743901058953537E00_BK, 8.56288474354474431428E-2_BK, 9.24408810558863637013E-4_BK]

real(bk), dimension(8), parameter	qp_y0 = [-6.05014350600728481186E00_BK, -5.14105326766599330220E01_BK, -1.47077505154951170175E02_BK, -1.77681167980488050595E02_BK, -9.32060152123768231369E01_BK, -1.95539544257735972385E01_BK, -1.28252718670509318512E00_BK, -1.13663838898469149931E-2_BK]

real(bk), dimension(8), parameter	qq_y0 = [2.42005740240291393179E02_BK, 2.06209331660327847417E03_BK, 5.93072701187316984827E03_BK, 7.24046774195652478189E03_BK, 3.88240183605401609683E03_BK, 8.56430025976980587198E02_BK, 6.43178256118178023184E01_BK, 1.00000000000000000000E00_BK]

real(bk), dimension(*), parameter	pp_j1 = [1.00000000000000000254E00_BK, 5.21451598682361504063E00_BK, 8.42404590141772420927E00_BK, 5.11207951146807644818E00_BK, 1.12719608129684925192E00_BK, 7.31397056940917570436E-2_BK, 7.62125616208173112003E-4_BK]

real(bk), dimension(*), parameter	pq_j1 = [9.99999999999999997461E-1_BK, 5.20982848682361821619E00_BK, 8.39985554327604159757E00_BK, 5.07386386128601488557E00_BK, 1.10514232634061696926E00_BK, 6.88455908754495404082E-2_BK, 5.71323128072548699714E-4_BK]

real(bk), dimension(*), parameter	qp_j1 = [2.52070205858023719784E01_BK, 2.11688757100572135698E2_BK, 5.97489612400613639965E02_BK, 7.10856304998926107277E2_BK, 3.66779609360150777800E02_BK, 7.58238284132545283818E1_BK, 4.98213872951233449420E00_BK, 5.10862594750176621635E-2_BK]

real(bk), dimension(*), parameter	qq_j1 = [3.36093607810698293419E02_BK, 2.82619278517639096600E03_BK, 7.99704160447350683650E03_BK, 9.56231892404756170795E03_BK, 4.98641058337653607651E03_BK, 1.05644886038262816351E03_BK, 7.42373277035675149943E01_BK, ONE]

real(bk), dimension(*), parameter	yp_y1 = [-7.78877196265950026825E17_BK, 2.02439475713594898196E17_BK, -8.12770255501325109621E15_BK, 1.14509511541823727583E14_BK, -6.47355876379160291031E11_BK, 1.26320474790178026440E09_BK]

real(bk), dimension(*), parameter	yq_y1 = [3.97270608116560655612E18_BK, 6.87141087355300489866E16_BK, 6.20557727146953693363E14_BK, 3.88231277496238566008E12_BK, 1.87601316108706159478E10_BK, 7.34811944459721705660E07_BK, 2.35564092943068577943E05_BK, 5.94301592346128195359E02_BK, ONE]

real(bk), dimension(*), parameter	p1_k0 = [-1.372509002685546267e-1_BK, 2.574916117833312855e-1_BK, 1.395474602146869316e-2_BK, 5.445476986653926759e-4_BK, 7.125159422136622118e-6_BK]

real(bk), dimension(*), parameter	q1_k0 = [ 1.000000000000000000e+00_BK, -5.458333438017788530e-02_BK, 1.291052816975251298e-03_BK, -1.367653946978586591e-05_BK]

real(bk), parameter	y_k0 = 1.137250900268554688_BK

real(bk), parameter	y_k1 = 8.69547128677368164e-2_BK

real(bk), parameter	y2_k1 = 1.45034217834472656_BK

real(bk), dimension(*), parameter	p2_k0 = [ 1.159315156584124484e-01_BK, 2.789828789146031732e-01_BK, 2.524892993216121934e-02_BK, 8.460350907213637784e-04_BK, 1.491471924309617534e-05_BK, 1.627106892422088488e-07_BK, 1.208266102392756055e-09_BK, 6.611686391749704310e-12_BK]

real(bk), dimension(*), parameter	p3_k0 = [ 2.533141373155002416e-1_BK, 3.628342133984595192e0_BK, 1.868441889406606057e1_BK, 4.306243981063412784e1_BK, 4.424116209627428189e1_BK, 1.562095339356220468e1_BK, -1.810138978229410898e0_BK, -1.414237994269995877e0_BK, -9.369168119754924625e-2_BK]

real(bk), dimension(*), parameter	q3_k0 = [ONE, 1.494194694879908328e1_BK, 8.265296455388554217e1_BK, 2.162779506621866970e2_BK, 2.845145155184222157e2_BK, 1.851714491916334995e2_BK, 5.486540717439723515e1_BK, 6.118075837628957015e0_BK, 1.586261269326235053e-1_BK]

real(bk), dimension(*), parameter	p1_k1 = [-3.62137953440350228e-3_BK, 7.11842087490330300e-3_BK, 1.00302560256614306e-5_BK, 1.77231085381040811e-6_BK]

real(bk), dimension(*), parameter	q1_k1 = [1.00000000000000000e0_BK, -4.80414794429043831e-2_BK, 9.85972641934416525e-4_BK, -8.91196859397070326e-6_BK]

real(bk), dimension(*), parameter	p2_k1 = [-3.07965757829206184e-1_BK, -7.80929703673074907e-02_BK, -2.70619343754051620e-3_BK, -2.49549522229072008e-5_BK]

real(bk), dimension(*), parameter	q2_k1 = [1.00000000000000000e0_BK, -2.36316836412163098e-2_BK, 2.64524577525962719e-4_BK, -1.49749618004162787e-6_BK]

real(bk), dimension(*), parameter	p3_k1 = [-1.97028041029226295e-1_BK, -2.32408961548087617e0_BK, -7.98269784507699938e0_BK, -2.39968410774221632e0_BK, 3.28314043780858713e1_BK, 5.67713761158496058e1_BK, 3.30907788466509823e1_BK, 6.62582288933739787e0_BK, 3.08851840645286691e-1_BK]

real(bk), dimension(*), parameter	q3_k1 = [1.00000000000000000e0_BK, 1.41811409298826118e1_BK, 7.35979466317556420e1_BK, 1.77821793937080859e2_BK, 2.11014501598705982e2_BK, 1.19425262951064454e2_BK, 2.88448064302447607e1_BK, 2.27912927104139732e0_BK, 2.50358186953478678e-2_BK]

real(bk), dimension(*), parameter	besseli0_small_coefs = [0.9999999999999998_BK, 0.2500000000000052_BK, 0.027777777777755364_BK, 0.001736111111149161_BK, 6.94444444107536e-05_BK, 1.9290123635366806e-6_BK, 3.9367592765038015e-8_BK, 6.151201574092085e-10_BK, 7.593827956729909e-12_BK, 7.596677643342155e-14_BK, 6.255282299620455e-16_BK, 4.470993793303175e-18_BK, 2.1859737023077178e-20_BK, 2.0941557335286373e-22_BK]

real(bk), dimension(*), parameter	besseli0_med_coefs = [0.3989422804014326_BK, 0.04986778505064754_BK, 0.028050628512954097_BK, 0.02921968830978531_BK, 0.04466889626137549_BK, 0.10220642174207666_BK, -0.9937439085650689_BK, 91.25330271974727_BK, -4901.408890977662_BK, 199209.2752981982_BK, -6.181516298413396e6_BK, 1.4830278710991925e8_BK, -2.7695254643719645e9_BK, 4.0351394830842026e10_BK, -4.5768930327229974e11_BK, 4.0134844243070063e12_BK, -2.6862476523182016e13_BK, 1.3437999451218112e14_BK, -4.856333741437621e14_BK, 1.1962791200680235e15_BK, -1.796269414464399e15_BK, 1.239942074380968e15_BK]

real(bk), dimension(*), parameter	besseli0_large_coefs = [0.3989422804014327_BK, 0.04986778505003549_BK, 0.028050629664438713_BK, 0.029218603406797997_BK, 0.045199090067282434_BK]

real(bk), dimension(*), parameter	besseli1_small_coefs = [ 0.08333333333333334_BK, 0.006944444444444374_BK, 0.00034722222222248526_BK, 1.1574074073690356e-5_BK, 2.7557319253050506e-7_BK, 4.920949730519126e-9_BK, 6.834656365321179e-11_BK, 7.593985414952446e-13_BK, 6.904652315442046e-15_BK, 5.2213850252454655e-17_BK, 3.405120412140281e-19_BK, 1.6398527256182257e-21_BK, 1.3161876924566675e-23_BK]

real(bk), dimension(*), parameter	besseli1_med_coefs = [ 0.39894228040143276_BK, -0.149603355151029_BK, -0.04675104787903509_BK, -0.04090746353279043_BK, -0.05744911840910781_BK,-0.12283724006390319_BK, 1.0023632527650936_BK, -94.90954045770921_BK, 5084.06899084327_BK, -206253.5613716743_BK, 6.387439538535799e6_BK, -1.529244018923123e8_BK, 2.849523551208316e9_BK, -4.141884344471782e10_BK, 4.6860149658304974e11_BK, -4.097852944580042e12_BK, 2.7345051110005453e13_BK, -1.3634833112030364e14_BK, 4.909983186948892e14_BK, -1.2048200837913132e15_BK, 1.8014682382937435e15_BK, -1.2377987428989558e15_BK]

real(bk), dimension(*), parameter	besseli1_large_coefs = [ 0.39894228040143265, -0.14960335515036183, -0.0467510491854453, -0.04090618769936314, -0.05808395099511361]

real(bk), parameter	besseljy_large_argument_min = 20.0_BK

Function/Subroutine Documentation

◆ besselj_down_recurrence()

pure real(bk) function, dimension(2) bessels_constants::besselj_down_recurrence	(	real(bk), intent(in)	x,
		real(bk), intent(in)	jnu,
		real(bk), intent(in)	jnup1,
		real(bk), intent(in)	nu_start,
		real(bk), intent(in)	nu_end )

◆ besselj_power_series()

elemental real(bk) function bessels_constants::besselj_power_series	(	real(bk), intent(in)	nu,
		real(bk), intent(in)	x )

Here is the call graph for this function:

◆ besselj_series_cutoff128()

elemental logical function bessels_constants::besselj_series_cutoff128	(	real(real128), intent(in)	x,
		real(real128), intent(in)	nu )

◆ besselj_series_cutoff32()

elemental logical function bessels_constants::besselj_series_cutoff32	(	real(real32), intent(in)	x,
		real(real32), intent(in)	nu )

◆ besselj_series_cutoff64()

elemental logical function bessels_constants::besselj_series_cutoff64	(	real(real64), intent(in)	x,
		real(real64), intent(in)	nu )

◆ besselj_up_recurrence()

elemental subroutine bessels_constants::besselj_up_recurrence	(	real(bk), intent(in)	x,
		real(bk), intent(in)	jnu,
		real(bk), intent(in)	jnum1,
		real(bk), intent(in)	nu_start,
		real(bk), intent(in)	nu_end,
		real(bk), intent(out)	a,
		real(bk), intent(out)	b )

◆ besseljy_debye_cutoff128()

elemental logical function bessels_constants::besseljy_debye_cutoff128	(	real(real128), intent(in)	nu,
		real(real128), intent(in)	x )

◆ besseljy_debye_cutoff32()

elemental logical function bessels_constants::besseljy_debye_cutoff32	(	real(real32), intent(in)	nu,
		real(real32), intent(in)	x )

◆ besseljy_debye_cutoff64()

elemental logical function bessels_constants::besseljy_debye_cutoff64	(	real(real64), intent(in)	nu,
		real(real64), intent(in)	x )

◆ besseljy_debye_fit128()

elemental real(real128) function bessels_constants::besseljy_debye_fit128 ( real(real128), intent(in) x )

◆ besseljy_debye_fit32()

elemental real(real32) function bessels_constants::besseljy_debye_fit32 ( real(real32), intent(in) x )

◆ besseljy_debye_fit64()

elemental real(real64) function bessels_constants::besseljy_debye_fit64 ( real(real64), intent(in) x )

◆ besseljy_large_argument_cutoff()

elemental logical function bessels_constants::besseljy_large_argument_cutoff	(	real(bk), intent(in)	nu,
		real(bk), intent(in)	x )

Here is the call graph for this function:

◆ bessely_power_series()

elemental subroutine bessels_constants::bessely_power_series	(	real(bk), intent(in)	nu,
		real(bk), intent(in)	x,
		real(bk), intent(out)	y,
		real(bk), intent(out)	j )

◆ bessely_series_cutoff32()

elemental logical function bessels_constants::bessely_series_cutoff32	(	real(real32), intent(in)	nu,
		real(real32), intent(in)	x )

◆ bessely_series_cutoff64()

elemental logical function bessels_constants::bessely_series_cutoff64	(	real(real64), intent(in)	nu,
		real(real64), intent(in)	x )

◆ cbrt()

elemental real(bk) function bessels_constants::cbrt ( real(bk), intent(in) x )

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◆ clenshaw_chebyshev()

pure real(bk) function bessels_constants::clenshaw_chebyshev	(	real(bk), intent(in)	x,
		real(bk), dimension(:), intent(in)	c )

◆ evalpoly()

pure real(bk) function bessels_constants::evalpoly	(	integer, intent(in)	n,
		real(bk), intent(in)	x,
		real(bk), dimension(n), intent(in)	p )

◆ evalpoly4()

pure real(bk) function bessels_constants::evalpoly4	(	real(bk), intent(in)	x,
		real(bk), dimension(4), intent(in)	p )

◆ evalpoly5()

pure real(bk) function bessels_constants::evalpoly5	(	real(bk), intent(in)	x,
		real(bk), dimension(5), intent(in)	p )

◆ evalpoly7()

pure real(bk) function bessels_constants::evalpoly7	(	real(bk), intent(in)	x,
		real(bk), dimension(7), intent(in)	p )

◆ evalpoly8()

pure real(bk) function bessels_constants::evalpoly8	(	real(bk), intent(in)	x,
		real(bk), dimension(8), intent(in)	p )

◆ hankel_debye_cutoff128()

elemental logical function bessels_constants::hankel_debye_cutoff128	(	real(real128), intent(in)	nu,
		real(real128), intent(in)	x )

◆ hankel_debye_cutoff32()

elemental logical function bessels_constants::hankel_debye_cutoff32	(	real(real32), intent(in)	nu,
		real(real32), intent(in)	x )

◆ hankel_debye_cutoff64()

elemental logical function bessels_constants::hankel_debye_cutoff64	(	real(real64), intent(in)	nu,
		real(real64), intent(in)	x )

◆ hankel_debye_fit32()

elemental real(real32) function bessels_constants::hankel_debye_fit32 ( real(real32), intent(in) x )

◆ hankel_debye_fit64()

elemental real(real64) function bessels_constants::hankel_debye_fit64 ( real(real64), intent(in) x )

◆ isinteger()

elemental logical function bessels_constants::isinteger ( real(bk), intent(in) x )

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◆ muladd()

elemental real(bk) function bessels_constants::muladd	(	real(bk), intent(in)	a,
		real(bk), intent(in)	x,
		real(bk), intent(in)	y )

Variable Documentation

◆ besseli0_large_coefs

real(bk), dimension(*), parameter bessels_constants::besseli0_large_coefs = [0.3989422804014327_BK, 0.04986778505003549_BK, 0.028050629664438713_BK, 0.029218603406797997_BK, 0.045199090067282434_BK]

◆ besseli0_med_coefs

real(bk), dimension(*), parameter bessels_constants::besseli0_med_coefs = [0.3989422804014326_BK, 0.04986778505064754_BK, 0.028050628512954097_BK, 0.02921968830978531_BK, 0.04466889626137549_BK, 0.10220642174207666_BK, -0.9937439085650689_BK, 91.25330271974727_BK, -4901.408890977662_BK, 199209.2752981982_BK, -6.181516298413396e6_BK, 1.4830278710991925e8_BK, -2.7695254643719645e9_BK, 4.0351394830842026e10_BK, -4.5768930327229974e11_BK, 4.0134844243070063e12_BK, -2.6862476523182016e13_BK, 1.3437999451218112e14_BK, -4.856333741437621e14_BK, 1.1962791200680235e15_BK, -1.796269414464399e15_BK, 1.239942074380968e15_BK]

◆ besseli0_small_coefs

real(bk), dimension(*), parameter bessels_constants::besseli0_small_coefs = [0.9999999999999998_BK, 0.2500000000000052_BK, 0.027777777777755364_BK, 0.001736111111149161_BK, 6.94444444107536e-05_BK, 1.9290123635366806e-6_BK, 3.9367592765038015e-8_BK, 6.151201574092085e-10_BK, 7.593827956729909e-12_BK, 7.596677643342155e-14_BK, 6.255282299620455e-16_BK, 4.470993793303175e-18_BK, 2.1859737023077178e-20_BK, 2.0941557335286373e-22_BK]

◆ besseli1_large_coefs

real(bk), dimension(*), parameter bessels_constants::besseli1_large_coefs = [ 0.39894228040143265, -0.14960335515036183, -0.0467510491854453, -0.04090618769936314, -0.05808395099511361]

◆ besseli1_med_coefs

real(bk), dimension(*), parameter bessels_constants::besseli1_med_coefs = [ 0.39894228040143276_BK, -0.149603355151029_BK, -0.04675104787903509_BK, -0.04090746353279043_BK, -0.05744911840910781_BK,-0.12283724006390319_BK, 1.0023632527650936_BK, -94.90954045770921_BK, 5084.06899084327_BK, -206253.5613716743_BK, 6.387439538535799e6_BK, -1.529244018923123e8_BK, 2.849523551208316e9_BK, -4.141884344471782e10_BK, 4.6860149658304974e11_BK, -4.097852944580042e12_BK, 2.7345051110005453e13_BK, -1.3634833112030364e14_BK, 4.909983186948892e14_BK, -1.2048200837913132e15_BK, 1.8014682382937435e15_BK, -1.2377987428989558e15_BK]

◆ besseli1_small_coefs

real(bk), dimension(*), parameter bessels_constants::besseli1_small_coefs = [ 0.08333333333333334_BK, 0.006944444444444374_BK, 0.00034722222222248526_BK, 1.1574074073690356e-5_BK, 2.7557319253050506e-7_BK, 4.920949730519126e-9_BK, 6.834656365321179e-11_BK, 7.593985414952446e-13_BK, 6.904652315442046e-15_BK, 5.2213850252454655e-17_BK, 3.405120412140281e-19_BK, 1.6398527256182257e-21_BK, 1.3161876924566675e-23_BK]

◆ besseljy_large_argument_min

real(bk), parameter bessels_constants::besseljy_large_argument_min = 20.0_BK

◆ bessely_cheb_weights

real(bk), dimension(29,17), parameter bessels_constants::bessely_cheb_weights = reshape([ -0.030017698430846347_BK, 0.04841599615543705_BK, -0.06170112748210926_BK, 0.010992867154582408_BK, -0.03732304718455494_BK, -0.06704282983696781_BK, 0.05527054188949959_BK, 0.023931299324571078_BK, -0.01660982874247215_BK, -0.0038257184915278875_BK, 0.0024486563159734553_BK, 0.00036760669126412974_BK, -0.00022289024621774598_BK, -2.400043085835714e-5_BK, 1.3967165370379739e-5_BK, 1.1481395619070928e-6_BK, -6.449732666954525e-7_BK, -4.1980803435719734e-8_BK, 2.2894937763100794e-8_BK, 1.228873366161081e-9_BK, -6.497632451926297e-10_BK, -2.8492149116234243e-11_BK, 1.4818408405099196e-11_BK, 6.100556567848311e-13_BK, -2.9867774919978274e-13_BK, -6.185528280054444e-15_BK, 3.7311423791866865e-15_BK, 4.123685520036296e-16_BK, -1.3481279584734043e-16_BK, 0.04160742192322324_BK, 0.034668235600932615_BK, 0.11174468340078995_BK, -0.04099618095057443_BK, 0.1254503646682523_BK, -0.13898784797365799_BK, -0.09733131946545694_BK, 0.07149834579877713_BK, 0.023375835755720973_BK, -0.014572641168112577_BK, -0.002981779009597293_BK, 0.0016841968136507765_BK, 0.0002422436246301404_BK, -0.000127737004832643_BK, -1.3814377122225202e-5_BK, 6.9111332786206e-6_BK, 5.866764647818481e-7_BK, -2.8135569182003675e-7_BK, -1.9403344167501224e-8_BK, 8.972400084810467e-9_BK, 5.113342130666102e-10_BK, -2.2951010536509386e-10_BK, -1.1304711135449809e-11_BK, 4.905817815473565e-12_BK, 1.894873147278986e-13_BK, -8.217632923341561e-14_BK, -4.218847493575595e-15_BK, 1.6772297836301473e-15_BK, -7.137148015447435e-17_BK, 0.022713476918759194_BK, -0.03501714644493984_BK, 0.04900399934159489_BK, -0.004572920361822816_BK, 0.03414506477673644_BK, 0.0583364038403724_BK, -0.04624123224424829_BK, -0.02357706101501925_BK, 0.01424650161095809_BK, 0.004131847507694573_BK, -0.0021768978247202514_BK, -0.0004222406947531938_BK, 0.00020419469487529897_BK, 2.882041410641021e-5_BK, -1.3118879606205788e-5_BK, -1.419547866831786e-6_BK, 6.171197932015276e-7_BK, 5.3215526542899864e-8_BK, -2.2283397359466684e-8_BK, -1.5689346295358737e-9_BK, 6.370162334131838e-10_BK, 3.785641839686755e-11_BK, -1.4927226121841386e-11_BK, -7.280852508197353e-13_BK, 2.822365357297534e-13_BK, 1.4096858601066386e-14_BK, -5.194257722353411e-15_BK, -1.784287003861859e-17_BK, 1.784287003861859e-17_BK, -0.005482743163667869_BK, -0.0026156864489958096_BK, -0.013446106107341984_BK, 0.003959772572751581_BK, -0.013050739904566335_BK, 0.012785648905104951_BK, 0.012302789524159771_BK, -0.007125881422379595_BK, -0.0032178006311644504_BK, 0.0015436443743600617_BK, 0.0004291283948110706_BK, -0.00018601906106350898_BK, -3.5730026469563336e-5_BK, 1.4521000123576475e-5_BK, 2.0641877773886624e-6_BK, -8.0134383976041e-7_BK, -8.833134689166324e-8_BK, 3.3105750509021536e-8_BK, 2.9248427531622776e-9_BK, -1.0652720751644758e-9_BK, -7.761774457286969e-11_BK, 2.758318276166857e-11_BK, 1.6716350526024826e-12_BK, -5.818832518996889e-13_BK, -3.163144349623995e-14_BK, 1.0744381574921492e-14_BK, 3.598312124454748e-16_BK, -1.2688263138573217e-16_BK, -1.4373423086664974e-17_BK, -0.000821102524680051_BK, 0.001369166415512963_BK, -0.0017176445978307614_BK, -0.00038167202153855176_BK, -0.0010693704116036165_BK, -0.0034162564467415902_BK, 0.0019105668931819009_BK, 0.0015608651654028757_BK, -0.000662690872417737_BK, -0.00028896692147194577_BK, 0.00010910809251752316_BK, 3.0258725355010946e-5_BK, -1.0717669999955374e-5_BK, -2.0862028639579696e-6_BK, 7.091627814767861e-7_BK, 1.0306000805131983e-7_BK, -3.4017752731151496e-8_BK, -3.856023535105163e-9_BK, 1.2437339960318393e-9_BK, 1.1358064900927889e-10_BK, -3.594555586962962e-11_BK, -2.7016821319796643e-12_BK, 8.405911755350802e-13_BK, 5.4115690103654197e-14_BK, -1.660105584745862e-14_BK, -8.187894806610529e-16_BK, 2.462687791788503e-16_BK, 2.0816681711721685e-17_BK, -6.443258625056712e-18_BK, 0.0002240588217758784_BK, -2.139628782819116e-5_BK, 0.0004963922147532327_BK, -0.00011956525731319659_BK, 0.00038470659301256783_BK, -0.00022845214105494214_BK, -0.0004692565509103452_BK, 0.0001676797752522885_BK, 0.0001335452722506947_BK, -4.206397012022229e-5_BK, -1.847619067631446e-5_BK, 5.51981330361833e-6_BK, 1.5583457267047952e-6_BK, -4.525989246540121e-7_BK, -9.035200300660385e-8_BK, 2.5768522858261958e-8_BK, 3.852458639733455e-9_BK, -1.084135171755376e-9_BK, -1.2724325563785672e-10_BK, 3.5416192958546876e-11_BK, 3.3285729083723912e-12_BK, -9.174161771285542e-13_BK, -7.329222174604474e-14_BK, 2.0034423068009816e-14_BK, 1.2002737593513098e-15_BK, -3.2511254198458856e-16_BK, -2.7507757976203656e-17_BK, 6.753030674338285e-18_BK, -4.336808689942018e-19_BK, 4.6589086507212064e-6_BK, -1.419986317236695e-5_BK, 7.726102539451062e-6_BK, 2.5019808838475857e-5_BK, -5.353457546572625e-7_BK, 7.876549687169565e-5_BK, -1.996847202131808e-5_BK, -4.169957016198162e-5_BK, 9.924101147153856e-6_BK, 8.2415996393497e-6_BK, -1.9586527669761305e-6_BK, -8.849155270353938e-7_BK, 2.1145772481562803e-7_BK, 6.146714709097454e-8_BK, -1.4757833806872662e-8_BK, -3.0347995540046756e-9_BK, 7.310991241996968e-10_BK, 1.1291045426976899e-10_BK, -2.724231275323183e-11_BK, -3.306873481836321e-12_BK, 7.984081946667783e-13_BK, 7.777996686699921e-14_BK, -1.874952442498305e-14_BK, -1.5555232495803793e-15_BK, 3.750913580232083e-16_BK, 2.4244503044553087e-17_BK, -6.63977026881971e-18_BK, -8.441288342922856e-19_BK, 3.7947076036992655e-19_BK, -3.837876843131191e-6_BK, 1.5306249581045373e-6_BK, -7.808225833446716e-6_BK, 8.447928863780004e-7_BK, -4.570697567070479e-6_BK, -4.1982552639485557e-7_BK, 8.226238919809268e-6_BK, -9.86994172463081e-7_BK, -2.6319604894434756e-6_BK, 4.2742958932228587e-7_BK, 3.841104494715522e-7_BK, -7.011130365317191e-8_BK, -3.295984466784781e-8_BK, 6.37554898520718e-9_BK, 1.9212842748116095e-9_BK, -3.851870296260733e-10_BK, -8.157917257527438e-11_BK, 1.6727904537992146e-11_BK, 2.682049173124509e-12_BK, -5.589600448593574e-13_BK, -6.949400331178381e-14_BK, 1.4635958089930247e-14_BK, 1.5059865847402264e-15_BK, -3.216721361622551e-16_BK, -2.5000540452330927e-17_BK, 5.001971562950145e-18_BK, -1.961002277600456e-18_BK, 9.647251501576167e-19_BK, -6.969871108835386e-19_BK, 1.576952254652365e-7_BK, -9.540862698044819e-8_BK, 3.3917615684812697e-7_BK, -4.813870672453743e-7_BK, 2.6408257938646016e-7_BK, -8.568425702351827e-7_BK, -1.2996848292204935e-7_BK, 5.684699761362054e-7_BK, -2.7544597243559516e-8_BK, -1.247732596836196e-7_BK, 1.4090830850669181e-8_BK, 1.398591135642683e-8_BK, -1.991545843477106e-9_BK, -9.83479157367889e-10_BK, 1.5579619154787597e-10_BK, 4.8812239436949277e-11_BK, -8.259978073280919e-12_BK, -1.7977167324163993e-12_BK, 3.156743262349288e-13_BK, 5.3090323232950275e-14_BK, -9.680314873025469e-15_BK, -1.183751262421577e-15_BK, 2.1703251434347915e-16_BK, 2.5924059718442872e-17_BK, -5.649951767599685e-18_BK, 8.287120783728401e-19_BK, -1.0219906276273448e-18_BK, 2.5227968798668708e-18_BK, -1.4714172340874703e-18_BK, 2.8189276354316185e-8_BK, -8.524800253702236e-9_BK, 5.163074759458915e-8_BK, 1.7587774571193398e-8_BK, 1.5532689836449176e-8_BK, 4.569379005731088e-8_BK, -7.364565287663236e-8_BK, -1.3794427678087878e-8_BK, 2.8705869772299055e-8_BK, -2.180238319299374e-10_BK, -4.6124233142017096e-9_BK, 3.6839126250828555e-10_BK, 4.0853238049027397e-10_BK, -4.58540375117209e-11_BK, -2.4105895138400274e-11_BK, 3.1690572156845862e-12_BK, 1.025021315725097e-12_BK, -1.4748687505667043e-13_BK, -3.336472532024983e-14_BK, 5.062095043025821e-15_BK, 8.815484952439681e-16_BK, -1.390034081631452e-16_BK, -1.9199758208465145e-17_BK, 2.8599694051079214e-18_BK, 4.412739143428028e-19_BK, -1.4432387356775567e-18_BK, -2.3578466668818103e-18_BK, -8.403587813975867e-19_BK, -2.0135183203302226e-19_BK, -2.7963515253359716e-9_BK, 2.6599405451754447e-9_BK, -5.363225685883765e-9_BK, 3.919112883175106e-9_BK, -2.6445728931356353e-9_BK, 3.986389181091895e-9_BK, 4.369788563535614e-9_BK, -4.202468942903132e-9_BK, -8.620553821731379e-10_BK, 1.1190715605385904e-9_BK, 1.6458619897562414e-11_BK, -1.364556955782257e-10_BK, 7.770660894600997e-12_BK, 9.797565423719047e-12_BK, -8.709272762295716e-13_BK, -4.951317701122077e-13_BK, 5.5017193500686674e-14_BK, 1.7973668773098524e-14_BK, -2.186053134804191e-15_BK, -5.417976610912264e-16_BK, 7.265668497060572e-17_BK, 1.0657145676262853e-17_BK, -1.4951583811856726e-18_BK, 1.001165055851074e-19_BK, -4.215593642978497e-19_BK, -8.996650316071422e-19_BK, 1.1892060156355519e-18_BK, -5.459522028374813e-19_BK, -9.29316147844718e-19_BK, -2.869285397772589e-11_BK, -1.425452662669203e-10_BK, -1.4765859863811186e-11_BK, -3.584266980792905e-10_BK, 1.2630165211284162e-10_BK, -4.813898813698495e-10_BK, 2.9823341363420924e-10_BK, 2.736833504070133e-10_BK, -1.789940159530945e-10_BK, -3.709803166716433e-11_BK, 3.4844491459805023e-11_BK, 8.72681373200755e-13_BK, -3.2915591662608672e-12_BK, 1.3002232883748757e-13_BK, 1.9753949839973547e-13_BK, -1.4075604115824882e-14_BK, -8.601511614454014e-15_BK, 8.194975088384275e-16_BK, 2.6866096515073e-16_BK, -2.6539953077529138e-17_BK, -6.38116169641218e-18_BK, -1.8536358293679684e-18_BK, 4.749772369976817e-19_BK, -6.718043393812506e-19_BK, 1.608438964002761e-19_BK, 5.165497356149306e-20_BK, 2.605394963005647e-19_BK, 1.0581028516295723e-19_BK, 3.601100072898283e-19_BK, 1.7263987678277334e-11_BK, -1.3813366927208365e-11_BK, 2.934247457063122e-11_BK, -7.979165795689896e-12_BK, 4.195660738851445e-12_BK, 3.4756966192072763e-12_BK, -3.8868044414248185e-11_BK, 1.4360156231687025e-11_BK, 1.2343845937660092e-11_BK, -6.048594850472885e-12_BK, -1.1764419064241353e-12_BK, 8.840620586141411e-13_BK, 2.5310500957954275e-14_BK, -6.57823088425572e-14_BK, 1.5812120648028614e-15_BK, 3.437403053731452e-15_BK, -2.0773399722137888e-16_BK, -1.2502298901942747e-16_BK, 1.1188335458126739e-17_BK, 1.318770475529763e-18_BK, 1.826317128659254e-18_BK, -1.371135591032674e-18_BK, -7.556266590585322e-19_BK, -1.3319774595248458e-19_BK, -6.907940207156658e-20_BK, 1.774511101624311e-18_BK, -4.537139020388408e-20_BK, 4.949220345202049e-19_BK, -1.1868141638100254e-18_BK, -8.498193197325338e-13_BK, 1.953201750327066e-12_BK, -1.6836406424518253e-12_BK, 2.5267159459094905e-12_BK, -1.1786713409725903e-12_BK, 2.057320315641163e-12_BK, 2.5591575645466365e-13_BK, -2.0678475108903006e-12_BK, 5.290174964157149e-13_BK, 4.2270269001999225e-13_BK, -1.680245826111033e-13_BK, -2.838265511092047e-14_BK, 1.8427577852297096e-14_BK, 5.755842428415847e-16_BK, -1.1124766162836294e-15_BK, 1.08483878138819e-17_BK, 5.233365672134661e-17_BK, -4.1398608828316095e-18_BK, -1.5252680555707005e-18_BK, 1.5518391236648752e-21_BK, -1.914160606977295e-18_BK, -1.1560851262788287e-18_BK, 8.614032803477796e-19_BK, -2.4613082189127555e-18_BK, 2.3715585034500812e-18_BK, -7.375149035246488e-19_BK, 1.5108762141152207e-18_BK, -1.5506658311469656e-18_BK, 8.17023779980148e-19_BK, -2.5827236864549892e-14_BK, -3.4718790561504414e-14_BK, -2.2011098530056326e-14_BK, -9.110104031477491e-14_BK, 7.290507373316453e-14_BK, -1.234623611877002e-13_BK, 1.6275850841628636e-13_BK, 1.798444625683851e-14_BK, -8.154482889879963e-14_BK, 1.634453336575052e-14_BK, 1.129456516347965e-14_BK, -3.897439775077071e-15_BK, -5.305238116730616e-16_BK, 3.1481637373066765e-16_BK, 1.2762608430395386e-17_BK, -1.6640493419786607e-17_BK, 4.907490184278107e-19_BK, 3.285996490596493e-19_BK, -1.6693969668826682e-18_BK, -6.276996493483055e-19_BK, 2.2721860225308528e-18_BK, -1.0636166658032876e-18_BK, 5.4043840077706323e-20_BK, -6.733003923003965e-19_BK, 8.654687466171472e-19_BK, -1.6353891516146702e-18_BK, -1.1401886941945345e-18_BK, 1.806451000706121e-18_BK, 1.0454806663253078e-18_BK, 4.9388506677207545e-15_BK, -8.11264980108463e-15_BK, 8.15564695267678e-15_BK, -6.6179014247901285e-15_BK, 1.2560443562777774e-15_BK, -1.1626485837362674e-15_BK, -8.428647433288211e-15_BK, 8.040878625052107e-15_BK, 7.604076442794149e-16_BK, -2.509940602859596e-15_BK, 4.433411320740124e-16_BK, 2.4051574424535735e-16_BK, -7.97263854654364e-17_BK, -8.468775456115063e-18_BK, 3.0977204928150507e-18_BK, -2.763609694292828e-18_BK, -4.528057493615123e-18_BK, 8.090667992714159e-18_BK, -5.7670273029389466e-18_BK, 6.935237082901993e-18_BK, 2.3956539089710175e-18_BK, 3.5297683311975285e-18_BK, -2.6680862870119677e-19_BK, -1.124331067925833e-18_BK, -3.969891564639305e-18_BK, 3.4988194829519685e-18_BK, 8.636411459915624e-19_BK, -1.3895984430563314e-18_BK, 1.7657006809049643e-18_BK, -2.058125495426769e-16_BK, 6.08114692374987e-16_BK, -4.430737266654462e-16_BK, 7.070791826861885e-16_BK, -4.496672312473068e-16_BK, 4.992680927678948e-16_BK, -2.0005398723221536e-16_BK, -4.085152288266179e-16_BK, 2.963046065367326e-16_BK, 1.9081397648228198e-17_BK, -6.065778883208153e-17_BK, 1.2267254817829564e-17_BK, 2.5241246780253446e-18_BK, 5.364001077188067e-19_BK, -1.1151793774136653e-18_BK, -2.647497194530543e-19_BK, -9.99558548618923e-19_BK, 1.9545043306813755e-18_BK, 1.0295729550672243e-18_BK, 5.850363951633064e-19_BK, 2.039938658283451e-19_BK, -1.622964422184252e-18_BK, -2.1240860691038883e-18_BK, 2.0835979355758296e-18_BK, -1.5423943263121515e-19_BK, -5.576729517866199e-19_BK, -3.7259501367076117e-20_BK, -1.8905808347578018e-19_BK, -1.4869058365515489e-18_BK], [29,17])

◆ bk

integer, parameter bessels_constants::bk = real64

◆ bsize

integer, parameter bessels_constants::bsize = int32

◆ five

real(bk), parameter bessels_constants::five = 5.00_BK

◆ four

real(bk), parameter bessels_constants::four = 4.00_BK

◆ fourth

real(bk), parameter bessels_constants::fourth = 0.25_BK

◆ gamma_five_sixths

real(bk), parameter bessels_constants::gamma_five_sixths = gamma(5.0_BK*SIXTH)

◆ gamma_one_sixth

real(bk), parameter bessels_constants::gamma_one_sixth = gamma(SIXTH)

◆ gamma_one_third

real(bk), parameter bessels_constants::gamma_one_third = gamma(THIRD)

◆ gamma_two_thirds

real(bk), parameter bessels_constants::gamma_two_thirds = gamma(TWOTHD)

◆ half

real(bk), parameter bessels_constants::half = 0.50_BK

◆ im

complex(bk), parameter bessels_constants::im = (ZERO, ONE)

◆ j0_poly_pio2

real(bk), dimension(*), parameter bessels_constants::j0_poly_pio2 = [ +1.00000000000000000000_BK , -0.25000000000000000000_BK , +0.01562499999999994000_BK , -0.00043402777777725544_BK , +6.781684026082576000000e-6_BK , -6.781683757550061e-8_BK , 4.709479394601058e-10_BK , -2.4016837144506874e-12_BK , 9.104258208703104e-15_BK ]

◆ j0_polys

real(bk), dimension(14,16), parameter bessels_constants::j0_polys = reshape([ 0.0000000000000000000_BK, -0.5191474972894669_BK, 0.10793870175491979_BK, 0.05660177443794914_BK, -0.008657669593292222_BK, -0.0021942003590739974_BK, 0.0002643770365942964_BK, 4.37291931443113e-5_BK, -4.338825419759815e-6_BK, -5.304927679598406e-7_BK, 4.469819175606667e-8_BK, 4.3284827345621115e-9_BK, -3.135111000732148e-10_BK, -2.628876489517534e-11_BK, -0.402759395702553_BK, 2.476919088072758e-16_BK, 0.20137969785127532_BK, -0.017518715285670765_BK, -0.013352611033152278_BK, 0.0010359438492839443_BK, 0.00037218755624680334_BK,-2.4952042421113972e-5_BK, -5.776086353844158e-6_BK, 3.374317129436161e-7_BK, 5.727482259215452e-8_BK, -2.9561880489355444e-9_BK, -3.905845672635605e-10_BK, 1.971332566705736e-11_BK, 0.000000000000000000_BK, 0.34026480655836816_BK, -0.030820651425593214_BK, -0.05298855286760721_BK, 0.004631042145890388_BK, 0.002257440229081131_BK, -0.00017518572879518415_BK,-4.6521091062878115e-5_BK, 3.199785909661533e-6_BK, 5.716500268232186e-7_BK, -3.5112898510841466e-8_BK, -4.684643389757727e-9_BK, 2.562685034682206e-10_BK, 2.7958958795750104e-11_BK, 0.30011575252613254_BK, -1.6640272822046001e-16_BK,-0.15005787626306408_BK, 0.007129737603121546_BK, 0.011742619737383848_BK, -0.0006260583453094324_BK, -0.00035093119008693753_BK, 1.7929701912295164e-5_BK, 5.6239324892485754e-6_BK, -2.668437501970219e-7_BK, -5.6648488273749086e-8_BK, 2.48117399780498e-9_BK, 3.8876537586241154e-10_BK,-1.6657136713437192e-11_BK, 0.000000000000000000_BK, -0.27145229992838193_BK, 0.015684124960953488_BK, 0.044033774963413_BK, -0.0025093022271948434_BK, -0.0020603351551475315_BK, 0.00011243486771159352_BK, 4.482303558813413e-5_BK, -2.288390108003442e-6_BK, -5.679383588459768e-7_BK, 2.693939234375692e-8_BK, 4.737285529934781e-9_BK, -2.0612709555352797e-10_BK,-2.8163166483726606e-11_BK, -0.2497048770578432_BK, 1.1807897766765572e-16_BK, 0.12485243852891914_BK, -0.0040907858517059345_BK, -0.010102792347641438_BK, 0.00038536375952213334_BK, 0.00031859711440332953_BK,-1.2373899600646271e-5_BK, -5.3013932979548665e-6_BK, 2.001098153528186e-7_BK, 5.4711629662471434e-8_BK, -1.9724572531751518e-9_BK, -3.8121398193699247e-10_BK, 1.3667679743782715e-11_BK, 0.000000000000000000_BK, 0.23245983136472478_BK, -0.009857064513825458_BK, -0.03818600911162367_BK, 0.0016073972920762946_BK, 0.0018420433388794816_BK, -7.581358465623415e-5_BK, -4.159284549011371e-5_BK, 1.650645590334915e-6_BK, 5.425453494592871e-7_BK, -2.0556207467977526e-8_BK, -4.620018928884712e-9_BK, 1.642028058414746e-10_BK, 2.7701605444102412e-11_BK, 0.21835940724787295_BK, -8.89726402965429e-17_BK, -0.10917970362393398_BK, 0.0027314677279632535_BK, 0.008944552393700088_BK, -0.00026391472261453583_BK, -0.00028847875053074687_BK, 8.858193371737123e-6_BK, 4.9233776180403375e-6_BK, -1.5077786827161215e-7_BK, -5.190218733666561e-8_BK, 1.5539413886301204e-9_BK, 3.674809363354973e-10_BK, -1.1113645791216594e-11_BK, 0.00000000000000000_BK, -0.20654643307799603_BK, 0.006916736034268416_BK, 0.034115572697347704_BK, -0.001137276252948717_BK, -0.0016680057255530109_BK, 5.4841792064182565e-5_BK, 3.837965853474541e-5_BK, -1.2335804050962046e-6_BK, -5.106259295634553e-7_BK, 1.592333632709497e-8_BK, 4.423517565793139e-9_BK, -1.3138837384184105e-10_BK,-2.6809397212536384e-11_BK, -0.19646537146865717_BK, 6.979167865106427e-17_BK, 0.09823268573432613_BK, -0.001988037402152532_BK, -0.008095530671166083_BK, 0.00019440675128712672_BK, 0.0002640383898036336_BK, -6.666777683303928e-6_BK, -4.5715696772304925e-6_BK, 1.1666296153560847e-7_BK, 4.8913639696764225e-8_BK, -1.2379867207945651e-9_BK, -3.508930968415813e-10_BK, 9.07632091591013e-12_BK, 0.00000000000000000_BK, 0.18772880304043943_BK, -0.005194182350684612_BK, -0.031096513233785917_BK, 0.0008577442641273341_BK, 0.0015312251534677639_BK, -4.184307585284775e-5_BK, -3.5603170534217916e-5_BK, 9.58002109234601e-7_BK, 4.795250964600283e-7_BK, -1.263434500625308e-8_BK, -4.20550167685701e-9_BK, 1.065791122326672e-10_BK, 2.5727417675684577e-11_BK, 0.18006337534431555_BK, -5.638484737644332e-17_BK, -0.09003168767215539_BK, 0.0015299132863046024_BK, 0.0074441453680234426_BK, -0.00015060569680378768_BK, -0.0002443398416353605_BK, 5.227001519013193e-6_BK, 4.267152607972633e-6_BK, -9.295966007495808e-8_BK, -4.610438011417262e-8_BK, 1.0049092632275165e-9_BK, 3.339442682325105e-10_BK, -7.4991079301099e-12_BK, 0.00000000000000000_BK, -0.17326589422922986_BK, 0.004084217951979124_BK, 0.028749284970146657_BK, -0.0006761643016121907_BK, -0.0014215899173758441_BK, 3.320978125391802e-5_BK, 3.3264379323815026e-5_BK, -7.684444100376941e-7_BK, -4.515479818833484e-7_BK, 1.0271599456634145e-8_BK, 3.993903280527723e-9_BK, -8.793975528824604e-11_BK, -2.4610374225652004e-11_BK, -0.16718460047381803_BK, 4.662597138876655e-17_BK, 0.08359230023690671_BK, -0.0012242529339116864_BK, -0.006925682915280748_BK, 0.00012100729852042988_BK, 0.00022821854128498174_BK,-4.230799709959437e-6_BK, -4.007618360337058e-6_BK, 7.601217108010105e-8_BK, 4.358483157250522e-8_BK, -8.317621452517008e-10_BK, -3.178805429572483e-10_BK, 6.284538399593043e-12_BK, 0.000000000000000000_BK, 0.16170155068925002_BK, -0.0033200234006036146_BK, -0.02685937038656159_BK, 0.0005505380905909195_BK, 0.0013316994659124243_BK, -2.715683205388875e-5_BK, -3.1289544794362e-5_BK, 6.326900360777323e-7_BK, 4.2697141781883964e-7_BK, -8.532447325590315e-9_BK, -3.799009445641295e-9_BK, 7.379552811590934e-11_BK, 2.353654960834717e-11_BK, 0.15672498625285222_BK, 1.1464880342445208e-19_BK,-0.07836249312642612_BK, 0.0010083833270351796_BK, 0.006501011610557426_BK, -9.993664895655577e-5_BK, -0.00021478298462967253_BK, 3.511086890959515e-6_BK, 3.7857022791122945e-6_BK, -6.350944888510364e-8_BK, -4.135588012575766e-8_BK, 7.135988717747828e-10_BK, 3.2075281131621564e-10_BK, 2.208506585533542e-12_BK], [14,16])

◆ j0_roots

real(bk), dimension(2,16), parameter bessels_constants::j0_roots = reshape([ 2.4048255576957730_BK, -1.1766916515308940e-16_BK, 3.8317059702075125_BK, -1.5269184090088067e-16_BK, 5.5200781102863110_BK, +8.0885971461467220e-17_BK, 7.0155866698156190_BK, -9.4141656534103890e-17_BK, 8.6537279129110130_BK, -2.9281260732077900e-16_BK, 10.173468135062722_BK, +4.4821622747688880e-16_BK, 11.791534439014281_BK, +2.8129569127787350e-16_BK, 13.323691936314223_BK, +2.6004080647188130e-16_BK, 14.930917708487787_BK, -7.0705145059830740e-16_BK, 16.470630050877634_BK, -1.6190195447981280e-15_BK, 18.071063967910924_BK, -9.6580480894262090e-16_BK, 19.615858510468243_BK, -1.0044456345266160e-15_BK, 21.211636629879260_BK, +4.9470774287840680e-16_BK, 22.760084380592772_BK, -4.9257493736149220e-16_BK, 24.352471530749302_BK, +9.1690671339510660e-16_BK, 25.903672087618382_BK, +4.8945307264198250e-16_BK], [2,16])

◆ j1_poly_pio2

real(bk), dimension(*), parameter bessels_constants::j1_poly_pio2 = [ 0.5_BK , -0.0624999999999989_BK , 0.002604166666657291_BK , -5.42534721917933e-5_BK , 6.781683542660179e-7_BK , -5.651361336587487e-9_BK , 3.36191211106159e-11_BK , -1.4511302591871352e-13_BK ]

◆ j1_polys

real(bk), dimension(14,16), parameter bessels_constants::j1_polys = reshape([ 0.5818652242815964_BK, 8.973834293036876e-17_BK, -0.20511071214777496_BK, 0.006058948324597746_BK, 0.013801769808047723_BK, -0.0003723170971916689_BK, -0.0003949590750416506_BK, 9.202953658715798e-6_BK, 6.267292697927347e-6_BK, -1.2681571675674473e-7_BK, -6.319326736018798e-8_BK, 1.057852721352679e-9_BK, 4.839653511789343e-10_BK, -2.1534683937074676e-11_BK, 0.0000000000000000000_BK, -0.402759395702553_BK, 0.05255614585697725_BK, 0.053410444132722765_BK, -0.005179719245639115_BK, -0.00223312533910116_BK, 0.00017466429071755533_BK, 4.6208700909637e-5_BK, -3.0368632747366735e-6_BK, -5.727790851165856e-7_BK, 3.248220586398651e-8_BK, 4.732693354840469e-9_BK, -2.346792988667587e-10_BK, -2.607612190048509e-11_BK, -0.34612620185379156_BK, 2.6002760076991505e-17_BK, 0.16697453550109428_BK, -0.009678268542879972_BK, -0.012099225779175138_BK, 0.0006654009006841076_BK, 0.0003541389011182841_BK, -1.742720356958137e-5_BK, -5.655294960447268e-6_BK, 2.484316221112215e-7_BK, 5.7101369594782676e-8_BK, -2.2587104440771904e-9_BK, -3.9854619701676605e-10_BK, 1.854508641982197e-11_BK, 0.00000000000000000000_BK, 0.30011575252613254_BK, -0.02138921280934146_BK, -0.04697047894974007_BK, 0.0031302917260424344_BK, 0.0021055871432169443_BK, -0.00012550790947431806_BK,-4.499147505171648e-5_BK, 2.401580334889493e-6_BK, 5.665260872870135e-7_BK, -2.7272058756924113e-8_BK, -4.718921752439826e-9_BK, 2.045523137027535e-10_BK, 2.6923755198436e-11_BK, 0.27329994163319987_BK, -1.3511933704624036e-16_BK,-0.13477468037992396_BK, 0.005116340346495344_BK, 0.010631861751990702_BK, -0.000448743683849691_BK, -0.0003268000185531749_BK, 1.3382556752353113e-5_BK, 5.363177082527157e-6_BK, -2.0647461181851255e-7_BK, -5.499892476485602e-8_BK, 1.9780335410646812e-9_BK, 3.8456897851545063e-10_BK,-1.5543946040865833e-11_BK, 0.0000000000000000000_BK, -0.2497048770578432_BK, 0.012272357555101388_BK, 0.04041116939079181_BK, -0.0019268187972545589_BK, -0.0019115826893618788_BK, 8.661729445925766e-5_BK, 4.241116264477775e-5_BK, -1.800978985430059e-6_BK, -5.47159694982648e-7_BK, 2.1682608288127194e-8_BK, 4.629875997238198e-9_BK, -1.6946465290961774e-10_BK,-2.7001263147077087e-11_BK, -0.23330441717143408_BK, 1.3347222236161232e-16_BK, 0.11580092244607755_BK, -0.0032489977328297747_BK, -0.009372527206041913_BK, 0.0003036138212749204_BK, 0.00029804555521007126_BK,-9.813819271763006e-6_BK, -5.0242293237237345e-6_BK, 1.6136482548346424e-7_BK, 5.251755806094281e-8_BK, -1.6213723779041528e-9_BK, -3.7130918416720704e-10_BK, 1.2840797195120732e-11_BK, 0.00000000000000000000_BK, 0.21835940724787295_BK, -0.008194403183877394_BK, -0.03577820957502993_BK, 0.001319573612804675_BK, 0.0017308725061602815_BK, -6.200735153951766e-5_BK, -3.938703730297954e-5_BK, 1.3569938030086903e-6_BK, 5.190652330962483e-7_BK, -1.7082573736581586e-8_BK, -4.464580500726025e-9_BK, 1.3835552663370753e-10_BK, 2.6508049073606443e-11_BK, 0.20701265272531905_BK, -1.1572365385200866e-16_BK,-0.10303781563402706_BK, 0.002289729546293356_BK, 0.008432435058846974_BK, -0.00021965941971569214_BK, -0.000272721543802475_BK, 7.36909520166486e-6_BK, 4.682127415369e-6_BK, -1.2611406291992532e-7_BK, -4.9733737497256667e-8_BK, 1.313333637862963e-9_BK, 3.5584811981981077e-10_BK,-1.0581432980865016e-11_BK, 0.00000000000000000000_BK,-0.19646537146865717_BK, 0.005964112206447895_BK, 0.032382122684890324_BK, -0.0009720337562254532_BK, -0.0015842303417456071_BK, 4.6667442166602986e-5_BK, 3.6572573450276185e-5_BK, -1.0499611641790313e-6_BK, -4.891787571238003e-7_BK, 1.3609422867092438e-8_BK, 4.2640592578446675e-9_BK, -1.1321195999108497e-10_BK,-2.5685037344174917e-11_BK, -0.18801748852581776_BK, 9.806595982257605e-17_BK, 0.09371909377243136_BK, -0.0017233243363111925_BK, -0.007714266760106843_BK, 0.00016755862384546863_BK, 0.000251827174474777_BK, -5.7335177376628445e-6_BK, -4.372425030172481e-6_BK, 1.0045839852031556e-7_BK, 4.698184959516747e-8_BK, -1.0717704296017814e-9_BK, -3.3952344362582674e-10_BK, 8.773851724781324e-12_BK, 0.00000000000000000000_BK, 0.18006337534431555_BK, -0.004589739858905968_BK, -0.029776581472313136_BK, 0.0007530284838491313_BK, 0.0014660390526475475_BK, -3.658900932751018e-5_BK, -3.4137236390211275e-5_BK, 8.366325091910564e-7_BK, 4.6108475352995054e-7_BK, -1.1047200388967438e-8_BK, -4.058793425595929e-9_BK, 9.363513647344476e-11_BK, 2.4720051360744732e-11_BK, 0.1734590492857464_BK, -8.319859584484218e-17_BK, -0.08653590193876039_BK, 0.0013568189856187354_BK, 0.007147216520714834_BK, -0.00013295776598760658_BK, -0.00023462959289705953_BK, 4.6031437800947915e-6_BK, 4.103196271673978e-6_BK, -8.18373301294018e-8_BK, -4.44403211204062e-8_BK, 8.872617322304839e-10_BK, 3.2359730989751983e-10_BK,-7.354373969368619e-12_BK, 0.00000000000000000000_BK,-0.16718460047381806_BK, 0.0036727588017285762_BK, 0.02770273166133465_BK, -0.0006050364924617241_BK, -0.0013693112504440895_BK, 2.9615596890234806e-5_BK, 3.206096184277923e-5_BK, -6.841058767433935e-7_BK, -4.358877331737043e-7_BK, 9.143763763164119e-9_BK, 3.864037532317281e-9_BK, -7.851667555762691e-11_BK, -2.3728757802646805e-11_BK, -0.1618382095526585_BK, 7.115722920799028e-17_BK, 0.08078219522574913_BK, -0.0011038527651152986_BK, -0.006686444726790514_BK, 0.00010870535083026479_BK, 0.00022030197347228358_BK,-3.791805814546456e-6_BK, -3.871147931227952e-6_BK, 6.80607764766372e-8_BK, 4.2160129307780366e-8_BK, -7.460427055677985e-10_BK, -3.0872139357605097e-10_BK, 6.24158293622982e-12_BK, 0.00000000000000000000_BK, 0.15672498625285222_BK, -0.0030251499811055965_BK, -0.026004046442225856_BK, 0.0004996832448037306_BK, 0.001288697907658241_BK, -2.457760943647847e-5_BK, -3.02856199504406e-5_BK, 5.715983781675481e-7_BK, 4.136275513873783e-7_BK, -7.703846567878601e-9_BK, -3.6853569596797437e-9_BK, 6.676439988396374e-11_BK, 2.277101500922319e-11_BK], [14,16])

◆ j1_roots

real(bk), dimension(2,16), parameter bessels_constants::j1_roots = reshape([ 1.8411837813406593_BK, +4.7898393919093694e-18_BK, 3.8317059702075125_BK, -1.5269184090088067e-16_BK, 5.3314427735250325_BK, +1.5109105349471405e-16_BK, 7.0155866698156190_BK, -9.4141656534103890e-17_BK, 8.5363163663462860_BK, -1.5433871213307537e-16_BK, 10.173468135062722_BK, +4.4821622747688880e-16_BK, 11.706004902592063_BK, +7.1213669422982460e-16_BK, 13.323691936314223_BK, +2.6004080647188130e-16_BK, 14.863588633909034_BK, -6.2657889887818790e-16_BK, 16.470630050877634_BK, -1.6190195447981280e-15_BK, 18.015527862681804_BK, -1.1196999448424267e-16_BK, 19.615858510468243_BK, -1.0044456345266160e-15_BK, 21.164369859188790_BK, +1.7024131380423588e-15_BK, 22.760084380592772_BK, -4.9257493736149220e-16_BK, 24.311326857210776_BK, -2.6147985585371720e-16_BK, 25.903672087618382_BK, +4.8945307264198250e-16_BK], [2,16])

◆ one

real(bk), parameter bessels_constants::one = 1.00_BK

◆ oneosqpi

real(bk), parameter bessels_constants::oneosqpi = ONE/SQRT(PI)

◆ p1_k0

real(bk), dimension(*), parameter bessels_constants::p1_k0 = [-1.372509002685546267e-1_BK, 2.574916117833312855e-1_BK, 1.395474602146869316e-2_BK, 5.445476986653926759e-4_BK, 7.125159422136622118e-6_BK]

◆ p1_k1

real(bk), dimension(*), parameter bessels_constants::p1_k1 = [-3.62137953440350228e-3_BK, 7.11842087490330300e-3_BK, 1.00302560256614306e-5_BK, 1.77231085381040811e-6_BK]

◆ p2_k0

real(bk), dimension(*), parameter bessels_constants::p2_k0 = [ 1.159315156584124484e-01_BK, 2.789828789146031732e-01_BK, 2.524892993216121934e-02_BK, 8.460350907213637784e-04_BK, 1.491471924309617534e-05_BK, 1.627106892422088488e-07_BK, 1.208266102392756055e-09_BK, 6.611686391749704310e-12_BK]

◆ p2_k1

real(bk), dimension(*), parameter bessels_constants::p2_k1 = [-3.07965757829206184e-1_BK, -7.80929703673074907e-02_BK, -2.70619343754051620e-3_BK, -2.49549522229072008e-5_BK]

◆ p3_k0

real(bk), dimension(*), parameter bessels_constants::p3_k0 = [ 2.533141373155002416e-1_BK, 3.628342133984595192e0_BK, 1.868441889406606057e1_BK, 4.306243981063412784e1_BK, 4.424116209627428189e1_BK, 1.562095339356220468e1_BK, -1.810138978229410898e0_BK, -1.414237994269995877e0_BK, -9.369168119754924625e-2_BK]

◆ p3_k1

real(bk), dimension(*), parameter bessels_constants::p3_k1 = [-1.97028041029226295e-1_BK, -2.32408961548087617e0_BK, -7.98269784507699938e0_BK, -2.39968410774221632e0_BK, 3.28314043780858713e1_BK, 5.67713761158496058e1_BK, 3.30907788466509823e1_BK, 6.62582288933739787e0_BK, 3.08851840645286691e-1_BK]

◆ pi

real(bk), parameter bessels_constants::pi = acos(-1.0_BK)

◆ pio2

real(bk), parameter bessels_constants::pio2 = PI*HALF

◆ pio4

real(bk), parameter bessels_constants::pio4 = PI*FOURTH

◆ pipow3o2

real(bk), parameter bessels_constants::pipow3o2 = PI * sqrt(PI)

◆ pp_j1

real(bk), dimension(*), parameter bessels_constants::pp_j1 = [1.00000000000000000254E00_BK, 5.21451598682361504063E00_BK, 8.42404590141772420927E00_BK, 5.11207951146807644818E00_BK, 1.12719608129684925192E00_BK, 7.31397056940917570436E-2_BK, 7.62125616208173112003E-4_BK]

◆ pp_y0

real(bk), dimension(7), parameter bessels_constants::pp_y0 = [9.99999999999999997821E-1_BK, 5.30324038235394892183E00_BK, 8.74716500199817011941E00_BK, 5.44725003058768775090E00_BK, 1.23953371646414299388E00_BK, 8.28352392107440799803E-2_BK, 7.96936729297347051624E-4_BK]

◆ pq_j1

real(bk), dimension(*), parameter bessels_constants::pq_j1 = [9.99999999999999997461E-1_BK, 5.20982848682361821619E00_BK, 8.39985554327604159757E00_BK, 5.07386386128601488557E00_BK, 1.10514232634061696926E00_BK, 6.88455908754495404082E-2_BK, 5.71323128072548699714E-4_BK]

◆ pq_y0

real(bk), dimension(7), parameter bessels_constants::pq_y0 = [1.00000000000000000218E00_BK, 5.30605288235394617618E00_BK, 8.76190883237069594232E00_BK, 5.47097740330417105182E00_BK, 1.25352743901058953537E00_BK, 8.56288474354474431428E-2_BK, 9.24408810558863637013E-4_BK]

◆ q1_k0

real(bk), dimension(*), parameter bessels_constants::q1_k0 = [ 1.000000000000000000e+00_BK, -5.458333438017788530e-02_BK, 1.291052816975251298e-03_BK, -1.367653946978586591e-05_BK]

◆ q1_k1

real(bk), dimension(*), parameter bessels_constants::q1_k1 = [1.00000000000000000e0_BK, -4.80414794429043831e-2_BK, 9.85972641934416525e-4_BK, -8.91196859397070326e-6_BK]

◆ q2_k1

real(bk), dimension(*), parameter bessels_constants::q2_k1 = [1.00000000000000000e0_BK, -2.36316836412163098e-2_BK, 2.64524577525962719e-4_BK, -1.49749618004162787e-6_BK]

◆ q3_k0

real(bk), dimension(*), parameter bessels_constants::q3_k0 = [ONE, 1.494194694879908328e1_BK, 8.265296455388554217e1_BK, 2.162779506621866970e2_BK, 2.845145155184222157e2_BK, 1.851714491916334995e2_BK, 5.486540717439723515e1_BK, 6.118075837628957015e0_BK, 1.586261269326235053e-1_BK]

◆ q3_k1

real(bk), dimension(*), parameter bessels_constants::q3_k1 = [1.00000000000000000e0_BK, 1.41811409298826118e1_BK, 7.35979466317556420e1_BK, 1.77821793937080859e2_BK, 2.11014501598705982e2_BK, 1.19425262951064454e2_BK, 2.88448064302447607e1_BK, 2.27912927104139732e0_BK, 2.50358186953478678e-2_BK]

◆ qp_j1

real(bk), dimension(*), parameter bessels_constants::qp_j1 = [2.52070205858023719784E01_BK, 2.11688757100572135698E2_BK, 5.97489612400613639965E02_BK, 7.10856304998926107277E2_BK, 3.66779609360150777800E02_BK, 7.58238284132545283818E1_BK, 4.98213872951233449420E00_BK, 5.10862594750176621635E-2_BK]

◆ qp_y0

real(bk), dimension(8), parameter bessels_constants::qp_y0 = [-6.05014350600728481186E00_BK, -5.14105326766599330220E01_BK, -1.47077505154951170175E02_BK, -1.77681167980488050595E02_BK, -9.32060152123768231369E01_BK, -1.95539544257735972385E01_BK, -1.28252718670509318512E00_BK, -1.13663838898469149931E-2_BK]

◆ qq_j1

real(bk), dimension(*), parameter bessels_constants::qq_j1 = [3.36093607810698293419E02_BK, 2.82619278517639096600E03_BK, 7.99704160447350683650E03_BK, 9.56231892404756170795E03_BK, 4.98641058337653607651E03_BK, 1.05644886038262816351E03_BK, 7.42373277035675149943E01_BK, ONE]

◆ qq_y0

real(bk), dimension(8), parameter bessels_constants::qq_y0 = [2.42005740240291393179E02_BK, 2.06209331660327847417E03_BK, 5.93072701187316984827E03_BK, 7.24046774195652478189E03_BK, 3.88240183605401609683E03_BK, 8.56430025976980587198E02_BK, 6.43178256118178023184E01_BK, 1.00000000000000000000E00_BK]

◆ six

real(bk), parameter bessels_constants::six = 6.00_BK

◆ sixth

real(bk), parameter bessels_constants::sixth = 1.0_BK/6.0_BK

◆ sq1o2pi

real(bk), parameter bessels_constants::sq1o2pi = 0.3989422804014326779399460599343818684758586311649346576659258296706579258993008_BK

◆ sq2o2

real(bk), parameter bessels_constants::sq2o2 = 0.707106781186547524400844362104849039284835937688474036588339868995366239231051_BK

◆ sq2opi

real(bk), parameter bessels_constants::sq2opi = 0.7978845608028653558798921198687637369517172623298693153318516593413158517986017_BK

◆ sq2pi

real(bk), parameter bessels_constants::sq2pi = 2.5066282746310007_BK

◆ sqpio2

real(bk), parameter bessels_constants::sqpio2 = 1.253314137315500251207882642405522626503493370304969158314961788171146827303924_BK

◆ third

real(bk), parameter bessels_constants::third = 1.0_BK/3.0_BK

◆ thpio4

real(bk), parameter bessels_constants::thpio4 = 2.35619449019234492885_BK

◆ three

real(bk), parameter bessels_constants::three = 3.00_BK

◆ two

real(bk), parameter bessels_constants::two = 2.00_BK

◆ twoopi

real(bk), parameter bessels_constants::twoopi = TWO/PI

◆ twothd

real(bk), parameter bessels_constants::twothd = 2.0_BK/3.0_BK

◆ y2_k1

real(bk), parameter bessels_constants::y2_k1 = 1.45034217834472656_BK

◆ y_k0

real(bk), parameter bessels_constants::y_k0 = 1.137250900268554688_BK

◆ y_k1

real(bk), parameter bessels_constants::y_k1 = 8.69547128677368164e-2_BK

◆ yp_y0

real(bk), dimension(8), parameter bessels_constants::yp_y0 = [-1.84950800436986690637E16_BK, 4.42733268572569800351E16_BK, -3.46628303384729719441E15_BK, 8.75906394395366999549E13_BK, -9.82136065717911466409E11_BK, 5.43526477051876500413E9_BK, -1.46639295903971606143E07_BK, 1.55924367855235737965E4_BK]

◆ yp_y1

real(bk), dimension(*), parameter bessels_constants::yp_y1 = [-7.78877196265950026825E17_BK, 2.02439475713594898196E17_BK, -8.12770255501325109621E15_BK, 1.14509511541823727583E14_BK, -6.47355876379160291031E11_BK, 1.26320474790178026440E09_BK]

◆ yq_y0

real(bk), dimension(8), parameter bessels_constants::yq_y0 = [2.50596256172653059228E17_BK, 3.17157752842975028269E15_BK, 2.02979612750105546709E13_BK, 8.64002487103935000337E10_BK, 2.68919633393814121987E08_BK, 6.26107330137134956842E05_BK, 1.04128353664259848412E03_BK, 1.00000000000000000000E00_BK]

◆ yq_y1

real(bk), dimension(*), parameter bessels_constants::yq_y1 = [3.97270608116560655612E18_BK, 6.87141087355300489866E16_BK, 6.20557727146953693363E14_BK, 3.88231277496238566008E12_BK, 1.87601316108706159478E10_BK, 7.34811944459721705660E07_BK, 2.35564092943068577943E05_BK, 5.94301592346128195359E02_BK, ONE]

◆ zero

real(bk), parameter bessels_constants::zero = 0.00_BK

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ besselj_down_recurrence()

◆ besselj_power_series()

◆ besselj_series_cutoff128()

◆ besselj_series_cutoff32()

◆ besselj_series_cutoff64()

◆ besselj_up_recurrence()

◆ besseljy_debye_cutoff128()

◆ besseljy_debye_cutoff32()

◆ besseljy_debye_cutoff64()

◆ besseljy_debye_fit128()

◆ besseljy_debye_fit32()

◆ besseljy_debye_fit64()

◆ besseljy_large_argument_cutoff()

◆ bessely_power_series()

◆ bessely_series_cutoff32()

◆ bessely_series_cutoff64()

◆ cbrt()

◆ clenshaw_chebyshev()

◆ evalpoly()

◆ evalpoly4()

◆ evalpoly5()

◆ evalpoly7()

◆ evalpoly8()

◆ hankel_debye_cutoff128()

◆ hankel_debye_cutoff32()

◆ hankel_debye_cutoff64()

◆ hankel_debye_fit32()

◆ hankel_debye_fit64()

◆ isinteger()

◆ muladd()

Variable Documentation

◆ besseli0_large_coefs

◆ besseli0_med_coefs

◆ besseli0_small_coefs

◆ besseli1_large_coefs

◆ besseli1_med_coefs

◆ besseli1_small_coefs

◆ besseljy_large_argument_min

◆ bessely_cheb_weights

◆ bk

◆ bsize

◆ five

◆ four

◆ fourth

◆ gamma_five_sixths

◆ gamma_one_sixth

◆ gamma_one_third

◆ gamma_two_thirds

◆ half

◆ im

◆ j0_poly_pio2

◆ j0_polys

◆ j0_roots

◆ j1_poly_pio2

◆ j1_polys

◆ j1_roots

◆ one

◆ oneosqpi

◆ p1_k0

◆ p1_k1

◆ p2_k0

◆ p2_k1

◆ p3_k0

◆ p3_k1

◆ pi

◆ pio2

◆ pio4

◆ pipow3o2

◆ pp_j1

◆ pp_y0

◆ pq_j1

◆ pq_y0

◆ q1_k0

◆ q1_k1

◆ q2_k1

◆ q3_k0