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/*
 * @(#)Coefficients.java        6.0.0    2024-05-19
 *
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package org.mariuszgromada.math.mxparser.mathcollection;

/**
 * Coefficients - various coefficients supporting numerical computation.
 *
 * @author         Mariusz Gromada

 *                 MathParser.org - mXparser project page

 *                 mXparser on GitHub

 *                 INFIMA place to purchase a commercial MathParser.org-mXparser software license

 *                 [email protected]

 *                 ScalarMath.org - a powerful math engine and math scripting language

 *                 Scalar Lite

 *                 Scalar Pro

 *                 MathSpace.pl

 *
 * @version        5.0.0
 */
final class Coefficients {
	/*
	 * --------------------------------------
	 * COEFFICIENTS FOR METHOD erfImp
	 * --------------------------------------
	*/
	/**
	 * Polynomial coefficients for a numerator of erfImp
	 * calculation for erf(x) in the interval [1e-10, 0.5].
	 */
	static final double[] erfImpAn = {
			0.00337916709551257388990745
			,-0.00073695653048167948530905
			,-0.374732337392919607868241
			,0.0817442448733587196071743
			,-0.0421089319936548595203468
			,0.0070165709512095756344528
			,-0.00495091255982435110337458
			,0.000871646599037922480317225
			};
	/**
	 * Polynomial coefficients for  adenominator of erfImp
	 * calculation for erf(x) in the interval [1e-10, 0.5].
	 */
	static final double[] erfImpAd = {
			1
			,-0.218088218087924645390535
			,0.412542972725442099083918
			,-0.0841891147873106755410271
			,0.0655338856400241519690695
			,-0.0120019604454941768171266
			,0.00408165558926174048329689
			,-0.000615900721557769691924509
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [0.5, 0.75].
	 */
	static final double[] erfImpBn = {
			-0.0361790390718262471360258
			,0.292251883444882683221149
			,0.281447041797604512774415
			,0.125610208862766947294894
			,0.0274135028268930549240776
			,0.00250839672168065762786937
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [0.5, 0.75].
	 */
	static final double[] erfImpBd = {
			1
			,1.8545005897903486499845
			,1.43575803037831418074962
			,0.582827658753036572454135
			,0.124810476932949746447682
			,0.0113724176546353285778481
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [0.75, 1.25].
	 */
	static final double[] erfImpCn = {
			-0.0397876892611136856954425
			,0.153165212467878293257683
			,0.191260295600936245503129
			,0.10276327061989304213645
			,0.029637090615738836726027
			,0.0046093486780275489468812
			,0.000307607820348680180548455
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [0.75, 1.25].
	 */
	static final double[] erfImpCd = {
			1
			,1.95520072987627704987886
			,1.64762317199384860109595
			,0.768238607022126250082483
			,0.209793185936509782784315
			,0.0319569316899913392596356
			,0.00213363160895785378615014
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [1.25, 2.25].
	 */
	static final double[] erfImpDn = {
			-0.0300838560557949717328341
			,0.0538578829844454508530552
			,0.0726211541651914182692959
			,0.0367628469888049348429018
			,0.00964629015572527529605267
			,0.00133453480075291076745275
			,0.778087599782504251917881e-4
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [1.25, 2.25].
	 */
	static final double[] erfImpDd = {
			1
			,1.75967098147167528287343
			,1.32883571437961120556307
			,0.552528596508757581287907
			,0.133793056941332861912279
			,0.0179509645176280768640766
			,0.00104712440019937356634038
			,-0.106640381820357337177643e-7
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [2.25, 3.5].
	 */
	static final double[] erfImpEn = {
			-0.0117907570137227847827732
			,0.014262132090538809896674
			,0.0202234435902960820020765
			,0.00930668299990432009042239
			,0.00213357802422065994322516
			,0.00025022987386460102395382
			,0.120534912219588189822126e-4
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [2.25, 3.5].
	 */
	static final double[] erfImpEd = {
			1
			,1.50376225203620482047419
			,0.965397786204462896346934
			,0.339265230476796681555511
			,0.0689740649541569716897427
			,0.00771060262491768307365526
			,0.000371421101531069302990367
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [3.5, 5.25].
	 */
	static final double[] erfImpFn = {
			-0.00546954795538729307482955
			,0.00404190278731707110245394
			,0.0054963369553161170521356
			,0.00212616472603945399437862
			,0.000394984014495083900689956
			,0.365565477064442377259271e-4
			,0.135485897109932323253786e-5
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [3.5, 5.25].
	 */
	static final double[] erfImpFd = {
			1
			,1.21019697773630784832251
			,0.620914668221143886601045
			,0.173038430661142762569515
			,0.0276550813773432047594539
			,0.00240625974424309709745382
			,0.891811817251336577241006e-4
			,-0.465528836283382684461025e-11
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [5.25, 8].
	 */
	static final double[] erfImpGn = {
			-0.00270722535905778347999196
			,0.0013187563425029400461378
			,0.00119925933261002333923989
			,0.00027849619811344664248235
			,0.267822988218331849989363e-4
			,0.923043672315028197865066e-6
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [5.25, 8].
	 */
	static final double[] erfImpGd = {
			1
			,0.814632808543141591118279
			,0.268901665856299542168425
			,0.0449877216103041118694989
			,0.00381759663320248459168994
			,0.000131571897888596914350697
			,0.404815359675764138445257e-11
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [8, 11.5].
	 */
	static final double[] erfImpHn = {
			-0.00109946720691742196814323
			,0.000406425442750422675169153
			,0.000274499489416900707787024
			,0.465293770646659383436343e-4
			,0.320955425395767463401993e-5
			,0.778286018145020892261936e-7
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [8, 11.5].
	 */
	static final double[] erfImpHd = {
			1, 0.588173710611846046373373
			,0.139363331289409746077541
			,0.0166329340417083678763028
			,0.00100023921310234908642639
			,0.24254837521587225125068e-4
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [11.5, 17].
	 */
	static final double[] erfImpIn = {
			-0.00056907993601094962855594
			,0.000169498540373762264416984
			,0.518472354581100890120501e-4
			,0.382819312231928859704678e-5
			,0.824989931281894431781794e-7
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [11.5, 17].
	 */
	static final double[] erfImpId = {
			1
			,0.339637250051139347430323
			,0.043472647870310663055044
			,0.00248549335224637114641629
			,0.535633305337152900549536e-4
			,-0.117490944405459578783846e-12
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [17, 24].
	 */
	static final double[] erfImpJn = {
			-0.000241313599483991337479091
			,0.574224975202501512365975e-4
			,0.115998962927383778460557e-4
			,0.581762134402593739370875e-6
			,0.853971555085673614607418e-8
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [17, 24].
	 */
	static final double[] erfImpJd = {
			1
			,0.233044138299687841018015
			,0.0204186940546440312625597
			,0.000797185647564398289151125
			,0.117019281670172327758019e-4
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [24, 38].
	 */
	static final double[] erfImpKn = {
			-0.000146674699277760365803642
			,0.162666552112280519955647e-4
			,0.269116248509165239294897e-5
			,0.979584479468091935086972e-7
			,0.101994647625723465722285e-8
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [24, 38].
	 */
	static final double[] erfImpKd = {
			1
			,0.165907812944847226546036
			,0.0103361716191505884359634
			,0.000286593026373868366935721
			,0.298401570840900340874568e-5
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [38, 60].
	 */
	static final double[] erfImpLn = {
			-0.583905797629771786720406e-4
			,0.412510325105496173512992e-5
			,0.431790922420250949096906e-6
			,0.993365155590013193345569e-8
			,0.653480510020104699270084e-10
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [38, 60].
	 */
	static final double[] erfImpLd = {
			1
			,0.105077086072039915406159
			,0.00414278428675475620830226
			,0.726338754644523769144108e-4
			,0.477818471047398785369849e-6
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [60, 85].
	 */
	static final double[] erfImpMn = {
			-0.196457797609229579459841e-4
			,0.157243887666800692441195e-5
			,0.543902511192700878690335e-7
			,0.317472492369117710852685e-9
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [60, 85].
	 */
	static final double[] erfImpMd = {
			1
			,0.052803989240957632204885
			,0.000926876069151753290378112
			,0.541011723226630257077328e-5
			,0.535093845803642394908747e-15
			};
	/**
	 * Polynomial coefficients for a numerator in erfImp
	 * calculation for erfc(x) in the interval [85, 110].
	 */
	static final double[] erfImpNn = {
			-0.789224703978722689089794e-5
			,0.622088451660986955124162e-6
			,0.145728445676882396797184e-7
			,0.603715505542715364529243e-10
			};
	/**
	 * Polynomial coefficients for a denominator in erfImp
	 * calculation for erfc(x) in the interval [85, 110].
	 */
	static final double[] erfImpNd = {
			1
			,0.0375328846356293715248719
			,0.000467919535974625308126054
			,0.193847039275845656900547e-5
			};
	/*
	 *
	 * 	--------------------------------------
	 * 	COEFFICIENTS FOR METHOD erfInvImp
	 * 	--------------------------------------
	 */
	/**
	 * Polynomial coefficients for a numerator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0, 0.5].
	 */
	static final double[] ervInvImpAn = {
			-0.000508781949658280665617
			,-0.00836874819741736770379
			,0.0334806625409744615033
			,-0.0126926147662974029034
			,-0.0365637971411762664006
			,0.0219878681111168899165
			,0.00822687874676915743155
			,-0.00538772965071242932965
			};
	/**
	 * Polynomial coefficients for a denominator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0, 0.5].
	 */
	static final double[] ervInvImpAd = {
			1
			,-0.970005043303290640362
			,-1.56574558234175846809
			,1.56221558398423026363
			,0.662328840472002992063
			,-0.71228902341542847553
			,-0.0527396382340099713954
			,0.0795283687341571680018
			,-0.00233393759374190016776
			,0.000886216390456424707504
			};
	/**
	 * Polynomial coefficients for a numerator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.5, 0.75].
	 */
	static final double[] ervInvImpBn = {
			-0.202433508355938759655
			,0.105264680699391713268
			,8.37050328343119927838
			,17.6447298408374015486
			,-18.8510648058714251895
			,-44.6382324441786960818
			,17.445385985570866523
			,21.1294655448340526258
			,-3.67192254707729348546
			};
	/**
	 * Polynomial coefficients for a denominator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.5, 0.75].
	 */
	static final double[] ervInvImpBd = {
			1
			,6.24264124854247537712
			,3.9713437953343869095
			,-28.6608180499800029974
			,-20.1432634680485188801
			,48.5609213108739935468
			,10.8268667355460159008
			,-22.6436933413139721736
			,1.72114765761200282724
			};
	/**
	 * Polynomial coefficients for a numerator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x less than 3.
	 */
	static final double[] ervInvImpCn = {
			-0.131102781679951906451
			,-0.163794047193317060787
			,0.117030156341995252019
			,0.387079738972604337464
			,0.337785538912035898924
			,0.142869534408157156766
			,0.0290157910005329060432
			,0.00214558995388805277169
			,-0.679465575181126350155e-6
			,0.285225331782217055858e-7
			,-0.681149956853776992068e-9
			};
	/**
	 * Polynomial coefficients for a denominator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x less than 3.
	 */
	static final double[] ervInvImpCd = {
			1
			,3.46625407242567245975
			,5.38168345707006855425
			,4.77846592945843778382
			,2.59301921623620271374
			,0.848854343457902036425
			,0.152264338295331783612
			,0.01105924229346489121
			};
	/**
	 * Polynomial coefficients for a numerator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x between 3 and 6.
	 */
	static final double[] ervInvImpDn = {
			-0.0350353787183177984712
			,-0.00222426529213447927281
			,0.0185573306514231072324
			,0.00950804701325919603619
			,0.00187123492819559223345
			,0.000157544617424960554631
			,0.460469890584317994083e-5
			,-0.230404776911882601748e-9
			,0.266339227425782031962e-11
			};
	/**
	 * Polynomial coefficients for a denominator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x between 3 and 6.
	 */
	static final double[] ervInvImpDd = {
			1
			,1.3653349817554063097
			,0.762059164553623404043
			,0.220091105764131249824
			,0.0341589143670947727934
			,0.00263861676657015992959
			,0.764675292302794483503e-4
			};
	/**
	 * Polynomial coefficients for a numerator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x between 6 and 18.
	 */
	static final double[] ervInvImpEn = {
			-0.0167431005076633737133
			,-0.00112951438745580278863
			,0.00105628862152492910091
			,0.000209386317487588078668
			,0.149624783758342370182e-4
			,0.449696789927706453732e-6
			,0.462596163522878599135e-8
			,-0.281128735628831791805e-13
			,0.99055709973310326855e-16
			};
	/**
	 * Polynomial coefficients for a denominator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x between 6 and 18.
	 */
	static final double[] ervInvImpEd = {
			1, 0.591429344886417493481
			,0.138151865749083321638
			,0.0160746087093676504695
			,0.000964011807005165528527
			,0.275335474764726041141e-4
			,0.282243172016108031869e-6
			};
	/**
	 * Polynomial coefficients for a numerator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x between 18 and 44.
	 */
	static final double[] ervInvImpFn = {
			-0.0024978212791898131227
			,-0.779190719229053954292e-5
			,0.254723037413027451751e-4
			,0.162397777342510920873e-5
			,0.396341011304801168516e-7
			,0.411632831190944208473e-9
			,0.145596286718675035587e-11
			,-0.116765012397184275695e-17
			};
	/**
	 * Polynomial coefficients for a denominator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x between 18 and 44.
	 */
	static final double[] ervInvImpFd = {
			1
			,0.207123112214422517181
			,0.0169410838120975906478
			,0.000690538265622684595676
			,0.145007359818232637924e-4
			,0.144437756628144157666e-6
			,0.509761276599778486139e-9
			};
	/**
	 * Polynomial coefficients for a numerator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x greater than 44.
	 */
	static final double[] ervInvImpGn = {
			-0.000539042911019078575891
			,-0.28398759004727721098e-6
			,0.899465114892291446442e-6
			,0.229345859265920864296e-7
			,0.225561444863500149219e-9
			,0.947846627503022684216e-12
			,0.135880130108924861008e-14
			,-0.348890393399948882918e-21
			};
	/**
	 * Polynomial coefficients for a denominator of erfInvImp
	 * calculation for erf^-1(z) in the interval [0.75, 1] with x greater than 44.
	 */
	static final double[] ervInvImpGd = {
			1
			,0.0845746234001899436914
			,0.00282092984726264681981
			,0.468292921940894236786e-4
			,0.399968812193862100054e-6
			,0.161809290887904476097e-8
			,0.231558608310259605225e-11
			};
	/**
	 * Supporting function
	 * while Exponential integral function Ei(x) calculation
	 */
	static final double[] EI = {
			1.915047433355013959531e2
			,4.403798995348382689974e2
			,1.037878290717089587658e3
			,2.492228976241877759138e3
			,6.071406374098611507965e3
			,1.495953266639752885229e4
			,3.719768849068903560439e4
			,9.319251363396537129882e4
			,2.349558524907683035782e5
			,5.955609986708370018502e5
			,1.516637894042516884433e6
			,3.877904330597443502996e6
			,9.950907251046844760026e6
			,2.561565266405658882048e7
			,6.612718635548492136250e7
			,1.711446713003636684975e8
			,4.439663698302712208698e8
			,1.154115391849182948287e9
			,3.005950906525548689841e9
			,7.842940991898186370453e9
			,2.049649711988081236484e10
			,5.364511859231469415605e10
			,1.405991957584069047340e11
			,3.689732094072741970640e11
			,9.694555759683939661662e11
			,2.550043566357786926147e12
			,6.714640184076497558707e12
			,1.769803724411626854310e13
			,4.669055014466159544500e13
			,1.232852079912097685431e14
			,3.257988998672263996790e14
			,8.616388199965786544948e14
			,2.280446200301902595341e15
			,6.039718263611241578359e15
			,1.600664914324504111070e16
			,4.244796092136850759368e16
			,1.126348290166966760275e17
			,2.990444718632336675058e17
			,7.943916035704453771510e17
			,2.111342388647824195000e18
			,5.614329680810343111535e18
			,1.493630213112993142255e19
			,3.975442747903744836007e19
			,1.058563689713169096306e20
		};
	/**
	 * Coefficients for Lanchos Gamma function approximation
	 */
	static final double[] lanchosGamma = {
			0.99999999999980993
			,676.5203681218851
			,-1259.1392167224028
			,771.32342877765313
			,-176.61502916214059
			,12.507343278686905
			,-0.13857109526572012
			,9.9843695780195716e-6
			,1.5056327351493116e-7
			};
	/**
	 * Coefficients for Log Gamma function approximation - A
	 */
	static final double[] logGammaA = {
			8.11614167470508450300E-4
			,-5.95061904284301438324E-4
			,7.93650340457716943945E-4
			,-2.77777777730099687205E-3
			,8.33333333333331927722E-2
			};
	/**
	 * Coefficients for Log Gamma function approximation - B
	 */
	static final double[] logGammaB = {
			-1.37825152569120859100E3
			,-3.88016315134637840924E4
			,-3.31612992738871184744E5
			,-1.16237097492762307383E6
			,-1.72173700820839662146E6
			,-8.53555664245765465627E5
			};
	/**
	 * Coefficients for Log Gamma function approximation - C
	 */
	static final double[] logGammaC = {
			-3.51815701436523470549E2
			,-1.70642106651881159223E4
			,-2.20528590553854454839E5
			,-1.13933444367982507207E6
			,-2.53252307177582951285E6
			,-2.01889141433532773231E6
			};
	/**
	 * Coefficients for Lambert W function, series for q near zero
	 */
	static final double[] lambertWqNearZero = {
			-1.0
			,2.331643981597124203363536062168
			,-1.812187885639363490240191647568
			,1.936631114492359755363277457668
			,-2.353551201881614516821543561516
			,3.066858901050631912893148922704
			,-4.175335600258177138854984177460
			,5.858023729874774148815053846119
			,-8.401032217523977370984161688514
			,12.250753501314460424
			,-18.100697012472442755
			,27.029044799010561650
			};
}