zunhj.f

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      SUBROUTINE ZUNHJ(ZR, ZI, FNU, IPMTR, TOL, PHIR, PHII, ARGR, ARGI,
     * ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
C***BEGIN PROLOGUE  ZUNHJ
C***REFER TO  ZBESI,ZBESK
C
C     REFERENCES
C         HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A.
C         STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9.
C
C         ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC
C         PRESS, N.Y., 1974, PAGE 420
C
C     ABSTRACT
C         ZUNHJ COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) =
C         J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU
C         BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION
C
C         C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) )
C
C         FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS
C         AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE.
C
C               (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2,
C
C         ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING
C         PURPOSES IN AIRY FUNCTIONS FROM CAIRY OR CBIRY.
C
C         MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND
C         MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR=
C         1 COMPUTES ALL EXCEPT ASUM AND BSUM.
C
C***ROUTINES CALLED  XZABS,ZDIV,XZLOG,XZSQRT,D1MACH
C***END PROLOGUE  ZUNHJ
C     COMPLEX ARG,ASUM,BSUM,CFNU,CONE,CR,CZERO,DR,P,PHI,PRZTH,PTFN,
C    *RFN13,RTZTA,RZTH,SUMA,SUMB,TFN,T2,UP,W,W2,Z,ZA,ZB,ZC,ZETA,ZETA1,
C    *ZETA2,ZTH
      DOUBLE PRECISION ALFA, ANG, AP, AR, ARGI, ARGR, ASUMI, ASUMR,
     * ATOL, AW2, AZTH, BETA, BR, BSUMI, BSUMR, BTOL, C, CONEI, CONER,
     * CRI, CRR, DRI, DRR, EX1, EX2, FNU, FN13, FN23, GAMA, GPI, HPI,
     * PHII, PHIR, PI, PP, PR, PRZTHI, PRZTHR, PTFNI, PTFNR, RAW, RAW2,
     * RAZTH, RFNU, RFNU2, RFN13, RTZTI, RTZTR, RZTHI, RZTHR, STI, STR,
     * SUMAI, SUMAR, SUMBI, SUMBR, TEST, TFNI, TFNR, THPI, TOL, TZAI,
     * TZAR, T2I, T2R, UPI, UPR, WI, WR, W2I, W2R, ZAI, ZAR, ZBI, ZBR,
     * ZCI, ZCR, ZEROI, ZEROR, ZETAI, ZETAR, ZETA1I, ZETA1R, ZETA2I,
     * ZETA2R, ZI, ZR, ZTHI, ZTHR, XZABS, AC, D1MACH
      INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR,
     * LRP1, L1, L2, M, IDUM
      DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30),
     * AP(30), PR(30), PI(30), UPR(14), UPI(14), CRR(14), CRI(14),
     * DRR(14), DRI(14)
      DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7), AR(8),
     1     AR(9), AR(10), AR(11), AR(12), AR(13), AR(14)/
     2     1.00000000000000000D+00,     1.04166666666666667D-01,
     3     8.35503472222222222D-02,     1.28226574556327160D-01,
     4     2.91849026464140464D-01,     8.81627267443757652D-01,
     5     3.32140828186276754D+00,     1.49957629868625547D+01,
     6     7.89230130115865181D+01,     4.74451538868264323D+02,
     7     3.20749009089066193D+03,     2.40865496408740049D+04,
     8     1.98923119169509794D+05,     1.79190200777534383D+06/
      DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7), BR(8),
     1     BR(9), BR(10), BR(11), BR(12), BR(13), BR(14)/
     2     1.00000000000000000D+00,    -1.45833333333333333D-01,
     3    -9.87413194444444444D-02,    -1.43312053915895062D-01,
     4    -3.17227202678413548D-01,    -9.42429147957120249D-01,
     5    -3.51120304082635426D+00,    -1.57272636203680451D+01,
     6    -8.22814390971859444D+01,    -4.92355370523670524D+02,
     7    -3.31621856854797251D+03,    -2.48276742452085896D+04,
     8    -2.04526587315129788D+05,    -1.83844491706820990D+06/
      DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10),
     1     C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18),
     2     C(19), C(20), C(21), C(22), C(23), C(24)/
     3     1.00000000000000000D+00,    -2.08333333333333333D-01,
     4     1.25000000000000000D-01,     3.34201388888888889D-01,
     5    -4.01041666666666667D-01,     7.03125000000000000D-02,
     6    -1.02581259645061728D+00,     1.84646267361111111D+00,
     7    -8.91210937500000000D-01,     7.32421875000000000D-02,
     8     4.66958442342624743D+00,    -1.12070026162229938D+01,
     9     8.78912353515625000D+00,    -2.36408691406250000D+00,
     A     1.12152099609375000D-01,    -2.82120725582002449D+01,
     B     8.46362176746007346D+01,    -9.18182415432400174D+01,
     C     4.25349987453884549D+01,    -7.36879435947963170D+00,
     D     2.27108001708984375D-01,     2.12570130039217123D+02,
     E    -7.65252468141181642D+02,     1.05999045252799988D+03/
      DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32),
     1     C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40),
     2     C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/
     3    -6.99579627376132541D+02,     2.18190511744211590D+02,
     4    -2.64914304869515555D+01,     5.72501420974731445D-01,
     5    -1.91945766231840700D+03,     8.06172218173730938D+03,
     6    -1.35865500064341374D+04,     1.16553933368645332D+04,
     7    -5.30564697861340311D+03,     1.20090291321635246D+03,
     8    -1.08090919788394656D+02,     1.72772750258445740D+00,
     9     2.02042913309661486D+04,    -9.69805983886375135D+04,
     A     1.92547001232531532D+05,    -2.03400177280415534D+05,
     B     1.22200464983017460D+05,    -4.11926549688975513D+04,
     C     7.10951430248936372D+03,    -4.93915304773088012D+02,
     D     6.07404200127348304D+00,    -2.42919187900551333D+05,
     E     1.31176361466297720D+06,    -2.99801591853810675D+06/
      DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56),
     1     C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64),
     2     C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/
     3     3.76327129765640400D+06,    -2.81356322658653411D+06,
     4     1.26836527332162478D+06,    -3.31645172484563578D+05,
     5     4.52187689813627263D+04,    -2.49983048181120962D+03,
     6     2.43805296995560639D+01,     3.28446985307203782D+06,
     7    -1.97068191184322269D+07,     5.09526024926646422D+07,
     8    -7.41051482115326577D+07,     6.63445122747290267D+07,
     9    -3.75671766607633513D+07,     1.32887671664218183D+07,
     A    -2.78561812808645469D+06,     3.08186404612662398D+05,
     B    -1.38860897537170405D+04,     1.10017140269246738D+02,
     C    -4.93292536645099620D+07,     3.25573074185765749D+08,
     D    -9.39462359681578403D+08,     1.55359689957058006D+09,
     E    -1.62108055210833708D+09,     1.10684281682301447D+09/
      DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80),
     1     C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88),
     2     C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/
     3    -4.95889784275030309D+08,     1.42062907797533095D+08,
     4    -2.44740627257387285D+07,     2.24376817792244943D+06,
     5    -8.40054336030240853D+04,     5.51335896122020586D+02,
     6     8.14789096118312115D+08,    -5.86648149205184723D+09,
     7     1.86882075092958249D+10,    -3.46320433881587779D+10,
     8     4.12801855797539740D+10,    -3.30265997498007231D+10,
     9     1.79542137311556001D+10,    -6.56329379261928433D+09,
     A     1.55927986487925751D+09,    -2.25105661889415278D+08,
     B     1.73951075539781645D+07,    -5.49842327572288687D+05,
     C     3.03809051092238427D+03,    -1.46792612476956167D+10,
     D     1.14498237732025810D+11,    -3.99096175224466498D+11,
     E     8.19218669548577329D+11,    -1.09837515608122331D+12/
      DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104),
     1     C(105)/
     2     1.00815810686538209D+12,    -6.45364869245376503D+11,
     3     2.87900649906150589D+11,    -8.78670721780232657D+10,
     4     1.76347306068349694D+10,    -2.16716498322379509D+09,
     5     1.43157876718888981D+08,    -3.87183344257261262D+06,
     6     1.82577554742931747D+04/
      DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5), ALFA(6),
     1     ALFA(7), ALFA(8), ALFA(9), ALFA(10), ALFA(11), ALFA(12),
     2     ALFA(13), ALFA(14), ALFA(15), ALFA(16), ALFA(17), ALFA(18),
     3     ALFA(19), ALFA(20), ALFA(21), ALFA(22)/
     4    -4.44444444444444444D-03,    -9.22077922077922078D-04,
     5    -8.84892884892884893D-05,     1.65927687832449737D-04,
     6     2.46691372741792910D-04,     2.65995589346254780D-04,
     7     2.61824297061500945D-04,     2.48730437344655609D-04,
     8     2.32721040083232098D-04,     2.16362485712365082D-04,
     9     2.00738858762752355D-04,     1.86267636637545172D-04,
     A     1.73060775917876493D-04,     1.61091705929015752D-04,
     B     1.50274774160908134D-04,     1.40503497391269794D-04,
     C     1.31668816545922806D-04,     1.23667445598253261D-04,
     D     1.16405271474737902D-04,     1.09798298372713369D-04,
     E     1.03772410422992823D-04,     9.82626078369363448D-05/
      DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26), ALFA(27), ALFA(28),
     1     ALFA(29), ALFA(30), ALFA(31), ALFA(32), ALFA(33), ALFA(34),
     2     ALFA(35), ALFA(36), ALFA(37), ALFA(38), ALFA(39), ALFA(40),
     3     ALFA(41), ALFA(42), ALFA(43), ALFA(44)/
     4     9.32120517249503256D-05,     8.85710852478711718D-05,
     5     8.42963105715700223D-05,     8.03497548407791151D-05,
     6     7.66981345359207388D-05,     7.33122157481777809D-05,
     7     7.01662625163141333D-05,     6.72375633790160292D-05,
     8     6.93735541354588974D-04,     2.32241745182921654D-04,
     9    -1.41986273556691197D-05,    -1.16444931672048640D-04,
     A    -1.50803558053048762D-04,    -1.55121924918096223D-04,
     B    -1.46809756646465549D-04,    -1.33815503867491367D-04,
     C    -1.19744975684254051D-04,    -1.06184319207974020D-04,
     D    -9.37699549891194492D-05,    -8.26923045588193274D-05,
     E    -7.29374348155221211D-05,    -6.44042357721016283D-05/
      DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48), ALFA(49), ALFA(50),
     1     ALFA(51), ALFA(52), ALFA(53), ALFA(54), ALFA(55), ALFA(56),
     2     ALFA(57), ALFA(58), ALFA(59), ALFA(60), ALFA(61), ALFA(62),
     3     ALFA(63), ALFA(64), ALFA(65), ALFA(66)/
     4    -5.69611566009369048D-05,    -5.04731044303561628D-05,
     5    -4.48134868008882786D-05,    -3.98688727717598864D-05,
     6    -3.55400532972042498D-05,    -3.17414256609022480D-05,
     7    -2.83996793904174811D-05,    -2.54522720634870566D-05,
     8    -2.28459297164724555D-05,    -2.05352753106480604D-05,
     9    -1.84816217627666085D-05,    -1.66519330021393806D-05,
     A    -1.50179412980119482D-05,    -1.35554031379040526D-05,
     B    -1.22434746473858131D-05,    -1.10641884811308169D-05,
     C    -3.54211971457743841D-04,    -1.56161263945159416D-04,
     D     3.04465503594936410D-05,     1.30198655773242693D-04,
     E     1.67471106699712269D-04,     1.70222587683592569D-04/
      DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70), ALFA(71), ALFA(72),
     1     ALFA(73), ALFA(74), ALFA(75), ALFA(76), ALFA(77), ALFA(78),
     2     ALFA(79), ALFA(80), ALFA(81), ALFA(82), ALFA(83), ALFA(84),
     3     ALFA(85), ALFA(86), ALFA(87), ALFA(88)/
     4     1.56501427608594704D-04,     1.36339170977445120D-04,
     5     1.14886692029825128D-04,     9.45869093034688111D-05,
     6     7.64498419250898258D-05,     6.07570334965197354D-05,
     7     4.74394299290508799D-05,     3.62757512005344297D-05,
     8     2.69939714979224901D-05,     1.93210938247939253D-05,
     9     1.30056674793963203D-05,     7.82620866744496661D-06,
     A     3.59257485819351583D-06,     1.44040049814251817D-07,
     B    -2.65396769697939116D-06,    -4.91346867098485910D-06,
     C    -6.72739296091248287D-06,    -8.17269379678657923D-06,
     D    -9.31304715093561232D-06,    -1.02011418798016441D-05,
     E    -1.08805962510592880D-05,    -1.13875481509603555D-05/
      DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92), ALFA(93), ALFA(94),
     1     ALFA(95), ALFA(96), ALFA(97), ALFA(98), ALFA(99), ALFA(100),
     2     ALFA(101), ALFA(102), ALFA(103), ALFA(104), ALFA(105),
     3     ALFA(106), ALFA(107), ALFA(108), ALFA(109), ALFA(110)/
     4    -1.17519675674556414D-05,    -1.19987364870944141D-05,
     5     3.78194199201772914D-04,     2.02471952761816167D-04,
     6    -6.37938506318862408D-05,    -2.38598230603005903D-04,
     7    -3.10916256027361568D-04,    -3.13680115247576316D-04,
     8    -2.78950273791323387D-04,    -2.28564082619141374D-04,
     9    -1.75245280340846749D-04,    -1.25544063060690348D-04,
     A    -8.22982872820208365D-05,    -4.62860730588116458D-05,
     B    -1.72334302366962267D-05,     5.60690482304602267D-06,
     C     2.31395443148286800D-05,     3.62642745856793957D-05,
     D     4.58006124490188752D-05,     5.24595294959114050D-05,
     E     5.68396208545815266D-05,     5.94349820393104052D-05/
      DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114), ALFA(115),
     1     ALFA(116), ALFA(117), ALFA(118), ALFA(119), ALFA(120),
     2     ALFA(121), ALFA(122), ALFA(123), ALFA(124), ALFA(125),
     3     ALFA(126), ALFA(127), ALFA(128), ALFA(129), ALFA(130)/
     4     6.06478527578421742D-05,     6.08023907788436497D-05,
     5     6.01577894539460388D-05,     5.89199657344698500D-05,
     6     5.72515823777593053D-05,     5.52804375585852577D-05,
     7     5.31063773802880170D-05,     5.08069302012325706D-05,
     8     4.84418647620094842D-05,     4.60568581607475370D-05,
     9    -6.91141397288294174D-04,    -4.29976633058871912D-04,
     A     1.83067735980039018D-04,     6.60088147542014144D-04,
     B     8.75964969951185931D-04,     8.77335235958235514D-04,
     C     7.49369585378990637D-04,     5.63832329756980918D-04,
     D     3.68059319971443156D-04,     1.88464535514455599D-04/
      DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134), ALFA(135),
     1     ALFA(136), ALFA(137), ALFA(138), ALFA(139), ALFA(140),
     2     ALFA(141), ALFA(142), ALFA(143), ALFA(144), ALFA(145),
     3     ALFA(146), ALFA(147), ALFA(148), ALFA(149), ALFA(150)/
     4     3.70663057664904149D-05,    -8.28520220232137023D-05,
     5    -1.72751952869172998D-04,    -2.36314873605872983D-04,
     6    -2.77966150694906658D-04,    -3.02079514155456919D-04,
     7    -3.12594712643820127D-04,    -3.12872558758067163D-04,
     8    -3.05678038466324377D-04,    -2.93226470614557331D-04,
     9    -2.77255655582934777D-04,    -2.59103928467031709D-04,
     A    -2.39784014396480342D-04,    -2.20048260045422848D-04,
     B    -2.00443911094971498D-04,    -1.81358692210970687D-04,
     C    -1.63057674478657464D-04,    -1.45712672175205844D-04,
     D    -1.29425421983924587D-04,    -1.14245691942445952D-04/
      DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154), ALFA(155),
     1     ALFA(156), ALFA(157), ALFA(158), ALFA(159), ALFA(160),
     2     ALFA(161), ALFA(162), ALFA(163), ALFA(164), ALFA(165),
     3     ALFA(166), ALFA(167), ALFA(168), ALFA(169), ALFA(170)/
     4     1.92821964248775885D-03,     1.35592576302022234D-03,
     5    -7.17858090421302995D-04,    -2.58084802575270346D-03,
     6    -3.49271130826168475D-03,    -3.46986299340960628D-03,
     7    -2.82285233351310182D-03,    -1.88103076404891354D-03,
     8    -8.89531718383947600D-04,     3.87912102631035228D-06,
     9     7.28688540119691412D-04,     1.26566373053457758D-03,
     A     1.62518158372674427D-03,     1.83203153216373172D-03,
     B     1.91588388990527909D-03,     1.90588846755546138D-03,
     C     1.82798982421825727D-03,     1.70389506421121530D-03,
     D     1.55097127171097686D-03,     1.38261421852276159D-03/
      DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174), ALFA(175),
     1     ALFA(176), ALFA(177), ALFA(178), ALFA(179), ALFA(180)/
     2     1.20881424230064774D-03,     1.03676532638344962D-03,
     3     8.71437918068619115D-04,     7.16080155297701002D-04,
     4     5.72637002558129372D-04,     4.42089819465802277D-04,
     5     3.24724948503090564D-04,     2.20342042730246599D-04,
     6     1.28412898401353882D-04,     4.82005924552095464D-05/
      DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5), BETA(6),
     1     BETA(7), BETA(8), BETA(9), BETA(10), BETA(11), BETA(12),
     2     BETA(13), BETA(14), BETA(15), BETA(16), BETA(17), BETA(18),
     3     BETA(19), BETA(20), BETA(21), BETA(22)/
     4     1.79988721413553309D-02,     5.59964911064388073D-03,
     5     2.88501402231132779D-03,     1.80096606761053941D-03,
     6     1.24753110589199202D-03,     9.22878876572938311D-04,
     7     7.14430421727287357D-04,     5.71787281789704872D-04,
     8     4.69431007606481533D-04,     3.93232835462916638D-04,
     9     3.34818889318297664D-04,     2.88952148495751517D-04,
     A     2.52211615549573284D-04,     2.22280580798883327D-04,
     B     1.97541838033062524D-04,     1.76836855019718004D-04,
     C     1.59316899661821081D-04,     1.44347930197333986D-04,
     D     1.31448068119965379D-04,     1.20245444949302884D-04,
     E     1.10449144504599392D-04,     1.01828770740567258D-04/
      DATA BETA(23), BETA(24), BETA(25), BETA(26), BETA(27), BETA(28),
     1     BETA(29), BETA(30), BETA(31), BETA(32), BETA(33), BETA(34),
     2     BETA(35), BETA(36), BETA(37), BETA(38), BETA(39), BETA(40),
     3     BETA(41), BETA(42), BETA(43), BETA(44)/
     4     9.41998224204237509D-05,     8.74130545753834437D-05,
     5     8.13466262162801467D-05,     7.59002269646219339D-05,
     6     7.09906300634153481D-05,     6.65482874842468183D-05,
     7     6.25146958969275078D-05,     5.88403394426251749D-05,
     8    -1.49282953213429172D-03,    -8.78204709546389328D-04,
     9    -5.02916549572034614D-04,    -2.94822138512746025D-04,
     A    -1.75463996970782828D-04,    -1.04008550460816434D-04,
     B    -5.96141953046457895D-05,    -3.12038929076098340D-05,
     C    -1.26089735980230047D-05,    -2.42892608575730389D-07,
     D     8.05996165414273571D-06,     1.36507009262147391D-05,
     E     1.73964125472926261D-05,     1.98672978842133780D-05/
      DATA BETA(45), BETA(46), BETA(47), BETA(48), BETA(49), BETA(50),
     1     BETA(51), BETA(52), BETA(53), BETA(54), BETA(55), BETA(56),
     2     BETA(57), BETA(58), BETA(59), BETA(60), BETA(61), BETA(62),
     3     BETA(63), BETA(64), BETA(65), BETA(66)/
     4     2.14463263790822639D-05,     2.23954659232456514D-05,
     5     2.28967783814712629D-05,     2.30785389811177817D-05,
     6     2.30321976080909144D-05,     2.28236073720348722D-05,
     7     2.25005881105292418D-05,     2.20981015361991429D-05,
     8     2.16418427448103905D-05,     2.11507649256220843D-05,
     9     2.06388749782170737D-05,     2.01165241997081666D-05,
     A     1.95913450141179244D-05,     1.90689367910436740D-05,
     B     1.85533719641636667D-05,     1.80475722259674218D-05,
     C     5.52213076721292790D-04,     4.47932581552384646D-04,
     D     2.79520653992020589D-04,     1.52468156198446602D-04,
     E     6.93271105657043598D-05,     1.76258683069991397D-05/
      DATA BETA(67), BETA(68), BETA(69), BETA(70), BETA(71), BETA(72),
     1     BETA(73), BETA(74), BETA(75), BETA(76), BETA(77), BETA(78),
     2     BETA(79), BETA(80), BETA(81), BETA(82), BETA(83), BETA(84),
     3     BETA(85), BETA(86), BETA(87), BETA(88)/
     4    -1.35744996343269136D-05,    -3.17972413350427135D-05,
     5    -4.18861861696693365D-05,    -4.69004889379141029D-05,
     6    -4.87665447413787352D-05,    -4.87010031186735069D-05,
     7    -4.74755620890086638D-05,    -4.55813058138628452D-05,
     8    -4.33309644511266036D-05,    -4.09230193157750364D-05,
     9    -3.84822638603221274D-05,    -3.60857167535410501D-05,
     A    -3.37793306123367417D-05,    -3.15888560772109621D-05,
     B    -2.95269561750807315D-05,    -2.75978914828335759D-05,
     C    -2.58006174666883713D-05,    -2.41308356761280200D-05,
     D    -2.25823509518346033D-05,    -2.11479656768912971D-05,
     E    -1.98200638885294927D-05,    -1.85909870801065077D-05/
      DATA BETA(89), BETA(90), BETA(91), BETA(92), BETA(93), BETA(94),
     1     BETA(95), BETA(96), BETA(97), BETA(98), BETA(99), BETA(100),
     2     BETA(101), BETA(102), BETA(103), BETA(104), BETA(105),
     3     BETA(106), BETA(107), BETA(108), BETA(109), BETA(110)/
     4    -1.74532699844210224D-05,    -1.63997823854497997D-05,
     5    -4.74617796559959808D-04,    -4.77864567147321487D-04,
     6    -3.20390228067037603D-04,    -1.61105016119962282D-04,
     7    -4.25778101285435204D-05,     3.44571294294967503D-05,
     8     7.97092684075674924D-05,     1.03138236708272200D-04,
     9     1.12466775262204158D-04,     1.13103642108481389D-04,
     A     1.08651634848774268D-04,     1.01437951597661973D-04,
     B     9.29298396593363896D-05,     8.40293133016089978D-05,
     C     7.52727991349134062D-05,     6.69632521975730872D-05,
     D     5.92564547323194704D-05,     5.22169308826975567D-05,
     E     4.58539485165360646D-05,     4.01445513891486808D-05/
      DATA BETA(111), BETA(112), BETA(113), BETA(114), BETA(115),
     1     BETA(116), BETA(117), BETA(118), BETA(119), BETA(120),
     2     BETA(121), BETA(122), BETA(123), BETA(124), BETA(125),
     3     BETA(126), BETA(127), BETA(128), BETA(129), BETA(130)/
     4     3.50481730031328081D-05,     3.05157995034346659D-05,
     5     2.64956119950516039D-05,     2.29363633690998152D-05,
     6     1.97893056664021636D-05,     1.70091984636412623D-05,
     7     1.45547428261524004D-05,     1.23886640995878413D-05,
     8     1.04775876076583236D-05,     8.79179954978479373D-06,
     9     7.36465810572578444D-04,     8.72790805146193976D-04,
     A     6.22614862573135066D-04,     2.85998154194304147D-04,
     B     3.84737672879366102D-06,    -1.87906003636971558D-04,
     C    -2.97603646594554535D-04,    -3.45998126832656348D-04,
     D    -3.53382470916037712D-04,    -3.35715635775048757D-04/
      DATA BETA(131), BETA(132), BETA(133), BETA(134), BETA(135),
     1     BETA(136), BETA(137), BETA(138), BETA(139), BETA(140),
     2     BETA(141), BETA(142), BETA(143), BETA(144), BETA(145),
     3     BETA(146), BETA(147), BETA(148), BETA(149), BETA(150)/
     4    -3.04321124789039809D-04,    -2.66722723047612821D-04,
     5    -2.27654214122819527D-04,    -1.89922611854562356D-04,
     6    -1.55058918599093870D-04,    -1.23778240761873630D-04,
     7    -9.62926147717644187D-05,    -7.25178327714425337D-05,
     8    -5.22070028895633801D-05,    -3.50347750511900522D-05,
     9    -2.06489761035551757D-05,    -8.70106096849767054D-06,
     A     1.13698686675100290D-06,     9.16426474122778849D-06,
     B     1.56477785428872620D-05,     2.08223629482466847D-05,
     C     2.48923381004595156D-05,     2.80340509574146325D-05,
     D     3.03987774629861915D-05,     3.21156731406700616D-05/
      DATA BETA(151), BETA(152), BETA(153), BETA(154), BETA(155),
     1     BETA(156), BETA(157), BETA(158), BETA(159), BETA(160),
     2     BETA(161), BETA(162), BETA(163), BETA(164), BETA(165),
     3     BETA(166), BETA(167), BETA(168), BETA(169), BETA(170)/
     4    -1.80182191963885708D-03,    -2.43402962938042533D-03,
     5    -1.83422663549856802D-03,    -7.62204596354009765D-04,
     6     2.39079475256927218D-04,     9.49266117176881141D-04,
     7     1.34467449701540359D-03,     1.48457495259449178D-03,
     8     1.44732339830617591D-03,     1.30268261285657186D-03,
     9     1.10351597375642682D-03,     8.86047440419791759D-04,
     A     6.73073208165665473D-04,     4.77603872856582378D-04,
     B     3.05991926358789362D-04,     1.60315694594721630D-04,
     C     4.00749555270613286D-05,    -5.66607461635251611D-05,
     D    -1.32506186772982638D-04,    -1.90296187989614057D-04/
      DATA BETA(171), BETA(172), BETA(173), BETA(174), BETA(175),
     1     BETA(176), BETA(177), BETA(178), BETA(179), BETA(180),
     2     BETA(181), BETA(182), BETA(183), BETA(184), BETA(185),
     3     BETA(186), BETA(187), BETA(188), BETA(189), BETA(190)/
     4    -2.32811450376937408D-04,    -2.62628811464668841D-04,
     5    -2.82050469867598672D-04,    -2.93081563192861167D-04,
     6    -2.97435962176316616D-04,    -2.96557334239348078D-04,
     7    -2.91647363312090861D-04,    -2.83696203837734166D-04,
     8    -2.73512317095673346D-04,    -2.61750155806768580D-04,
     9     6.38585891212050914D-03,     9.62374215806377941D-03,
     A     7.61878061207001043D-03,     2.83219055545628054D-03,
     B    -2.09841352012720090D-03,    -5.73826764216626498D-03,
     C    -7.70804244495414620D-03,    -8.21011692264844401D-03,
     D    -7.65824520346905413D-03,    -6.47209729391045177D-03/
      DATA BETA(191), BETA(192), BETA(193), BETA(194), BETA(195),
     1     BETA(196), BETA(197), BETA(198), BETA(199), BETA(200),
     2     BETA(201), BETA(202), BETA(203), BETA(204), BETA(205),
     3     BETA(206), BETA(207), BETA(208), BETA(209), BETA(210)/
     4    -4.99132412004966473D-03,    -3.45612289713133280D-03,
     5    -2.01785580014170775D-03,    -7.59430686781961401D-04,
     6     2.84173631523859138D-04,     1.10891667586337403D-03,
     7     1.72901493872728771D-03,     2.16812590802684701D-03,
     8     2.45357710494539735D-03,     2.61281821058334862D-03,
     9     2.67141039656276912D-03,     2.65203073395980430D-03,
     A     2.57411652877287315D-03,     2.45389126236094427D-03,
     B     2.30460058071795494D-03,     2.13684837686712662D-03,
     C     1.95896528478870911D-03,     1.77737008679454412D-03,
     D     1.59690280765839059D-03,     1.42111975664438546D-03/
      DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5), GAMA(6),
     1     GAMA(7), GAMA(8), GAMA(9), GAMA(10), GAMA(11), GAMA(12),
     2     GAMA(13), GAMA(14), GAMA(15), GAMA(16), GAMA(17), GAMA(18),
     3     GAMA(19), GAMA(20), GAMA(21), GAMA(22)/
     4     6.29960524947436582D-01,     2.51984209978974633D-01,
     5     1.54790300415655846D-01,     1.10713062416159013D-01,
     6     8.57309395527394825D-02,     6.97161316958684292D-02,
     7     5.86085671893713576D-02,     5.04698873536310685D-02,
     8     4.42600580689154809D-02,     3.93720661543509966D-02,
     9     3.54283195924455368D-02,     3.21818857502098231D-02,
     A     2.94646240791157679D-02,     2.71581677112934479D-02,
     B     2.51768272973861779D-02,     2.34570755306078891D-02,
     C     2.19508390134907203D-02,     2.06210828235646240D-02,
     D     1.94388240897880846D-02,     1.83810633800683158D-02,
     E     1.74293213231963172D-02,     1.65685837786612353D-02/
      DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26), GAMA(27), GAMA(28),
     1     GAMA(29), GAMA(30)/
     2     1.57865285987918445D-02,     1.50729501494095594D-02,
     3     1.44193250839954639D-02,     1.38184805735341786D-02,
     4     1.32643378994276568D-02,     1.27517121970498651D-02,
     5     1.22761545318762767D-02,     1.18338262398482403D-02/
      DATA EX1, EX2, HPI, GPI, THPI /
     1     3.33333333333333333D-01,     6.66666666666666667D-01,
     2     1.57079632679489662D+00,     3.14159265358979324D+00,
     3     4.71238898038468986D+00/
      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
C
      RFNU = 1.0D0/FNU
C-----------------------------------------------------------------------
C     OVERFLOW TEST (Z/FNU TOO SMALL)
C-----------------------------------------------------------------------
      TEST = D1MACH(1)*1.0D+3
      AC = FNU*TEST
      IF (DABS(ZR).GT.AC .OR. DABS(ZI).GT.AC) GO TO 15
      ZETA1R = 2.0D0*DABS(DLOG(TEST))+FNU
      ZETA1I = 0.0D0
      ZETA2R = FNU
      ZETA2I = 0.0D0
      PHIR = 1.0D0
      PHII = 0.0D0
      ARGR = 1.0D0
      ARGI = 0.0D0
      RETURN
   15 CONTINUE
      ZBR = ZR*RFNU
      ZBI = ZI*RFNU
      RFNU2 = RFNU*RFNU
C-----------------------------------------------------------------------
C     COMPUTE IN THE FOURTH QUADRANT
C-----------------------------------------------------------------------
      FN13 = FNU**EX1
      FN23 = FN13*FN13
      RFN13 = 1.0D0/FN13
      W2R = CONER - ZBR*ZBR + ZBI*ZBI
      W2I = CONEI - ZBR*ZBI - ZBR*ZBI
      AW2 = XZABS(W2R,W2I)
      IF (AW2.GT.0.25D0) GO TO 130
C-----------------------------------------------------------------------
C     POWER SERIES FOR CABS(W2).LE.0.25D0
C-----------------------------------------------------------------------
      K = 1
      PR(1) = CONER
      PI(1) = CONEI
      SUMAR = GAMA(1)
      SUMAI = ZEROI
      AP(1) = 1.0D0
      IF (AW2.LT.TOL) GO TO 20
      DO 10 K=2,30
        PR(K) = PR(K-1)*W2R - PI(K-1)*W2I
        PI(K) = PR(K-1)*W2I + PI(K-1)*W2R
        SUMAR = SUMAR + PR(K)*GAMA(K)
        SUMAI = SUMAI + PI(K)*GAMA(K)
        AP(K) = AP(K-1)*AW2
        IF (AP(K).LT.TOL) GO TO 20
   10 CONTINUE
      K = 30
   20 CONTINUE
      KMAX = K
      ZETAR = W2R*SUMAR - W2I*SUMAI
      ZETAI = W2R*SUMAI + W2I*SUMAR
      ARGR = ZETAR*FN23
      ARGI = ZETAI*FN23
      CALL XZSQRT(SUMAR, SUMAI, ZAR, ZAI)
      CALL XZSQRT(W2R, W2I, STR, STI)
      ZETA2R = STR*FNU
      ZETA2I = STI*FNU
      STR = CONER + EX2*(ZETAR*ZAR-ZETAI*ZAI)
      STI = CONEI + EX2*(ZETAR*ZAI+ZETAI*ZAR)
      ZETA1R = STR*ZETA2R - STI*ZETA2I
      ZETA1I = STR*ZETA2I + STI*ZETA2R
      ZAR = ZAR + ZAR
      ZAI = ZAI + ZAI
      CALL XZSQRT(ZAR, ZAI, STR, STI)
      PHIR = STR*RFN13
      PHII = STI*RFN13
      IF (IPMTR.EQ.1) GO TO 120
C-----------------------------------------------------------------------
C     SUM SERIES FOR ASUM AND BSUM
C-----------------------------------------------------------------------
      SUMBR = ZEROR
      SUMBI = ZEROI
      DO 30 K=1,KMAX
        SUMBR = SUMBR + PR(K)*BETA(K)
        SUMBI = SUMBI + PI(K)*BETA(K)
   30 CONTINUE
      ASUMR = ZEROR
      ASUMI = ZEROI
      BSUMR = SUMBR
      BSUMI = SUMBI
      L1 = 0
      L2 = 30
      BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI))
      ATOL = TOL
      PP = 1.0D0
      IAS = 0
      IBS = 0
      IF (RFNU2.LT.TOL) GO TO 110
      DO 100 IS=2,7
        ATOL = ATOL/RFNU2
        PP = PP*RFNU2
        IF (IAS.EQ.1) GO TO 60
        SUMAR = ZEROR
        SUMAI = ZEROI
        DO 40 K=1,KMAX
          M = L1 + K
          SUMAR = SUMAR + PR(K)*ALFA(M)
          SUMAI = SUMAI + PI(K)*ALFA(M)
          IF (AP(K).LT.ATOL) GO TO 50
   40   CONTINUE
   50   CONTINUE
        ASUMR = ASUMR + SUMAR*PP
        ASUMI = ASUMI + SUMAI*PP
        IF (PP.LT.TOL) IAS = 1
   60   CONTINUE
        IF (IBS.EQ.1) GO TO 90
        SUMBR = ZEROR
        SUMBI = ZEROI
        DO 70 K=1,KMAX
          M = L2 + K
          SUMBR = SUMBR + PR(K)*BETA(M)
          SUMBI = SUMBI + PI(K)*BETA(M)
          IF (AP(K).LT.ATOL) GO TO 80
   70   CONTINUE
   80   CONTINUE
        BSUMR = BSUMR + SUMBR*PP
        BSUMI = BSUMI + SUMBI*PP
        IF (PP.LT.BTOL) IBS = 1
   90   CONTINUE
        IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 110
        L1 = L1 + 30
        L2 = L2 + 30
  100 CONTINUE
  110 CONTINUE
      ASUMR = ASUMR + CONER
      PP = RFNU*RFN13
      BSUMR = BSUMR*PP
      BSUMI = BSUMI*PP
  120 CONTINUE
      RETURN
C-----------------------------------------------------------------------
C     CABS(W2).GT.0.25D0
C-----------------------------------------------------------------------
  130 CONTINUE
      CALL XZSQRT(W2R, W2I, WR, WI)
      IF (WR.LT.0.0D0) WR = 0.0D0
      IF (WI.LT.0.0D0) WI = 0.0D0
      STR = CONER + WR
      STI = WI
      CALL ZDIV(STR, STI, ZBR, ZBI, ZAR, ZAI)
      CALL XZLOG(ZAR, ZAI, ZCR, ZCI, IDUM)
      IF (ZCI.LT.0.0D0) ZCI = 0.0D0
      IF (ZCI.GT.HPI) ZCI = HPI
      IF (ZCR.LT.0.0D0) ZCR = 0.0D0
      ZTHR = (ZCR-WR)*1.5D0
      ZTHI = (ZCI-WI)*1.5D0
      ZETA1R = ZCR*FNU
      ZETA1I = ZCI*FNU
      ZETA2R = WR*FNU
      ZETA2I = WI*FNU
      AZTH = XZABS(ZTHR,ZTHI)
      ANG = THPI
      IF (ZTHR.GE.0.0D0 .AND. ZTHI.LT.0.0D0) GO TO 140
      ANG = HPI
      IF (ZTHR.EQ.0.0D0) GO TO 140
      ANG = DATAN(ZTHI/ZTHR)
      IF (ZTHR.LT.0.0D0) ANG = ANG + GPI
  140 CONTINUE
      PP = AZTH**EX2
      ANG = ANG*EX2
      ZETAR = PP*DCOS(ANG)
      ZETAI = PP*DSIN(ANG)
      IF (ZETAI.LT.0.0D0) ZETAI = 0.0D0
      ARGR = ZETAR*FN23
      ARGI = ZETAI*FN23
      CALL ZDIV(ZTHR, ZTHI, ZETAR, ZETAI, RTZTR, RTZTI)
      CALL ZDIV(RTZTR, RTZTI, WR, WI, ZAR, ZAI)
      TZAR = ZAR + ZAR
      TZAI = ZAI + ZAI
      CALL XZSQRT(TZAR, TZAI, STR, STI)
      PHIR = STR*RFN13
      PHII = STI*RFN13
      IF (IPMTR.EQ.1) GO TO 120
      RAW = 1.0D0/DSQRT(AW2)
      STR = WR*RAW
      STI = -WI*RAW
      TFNR = STR*RFNU*RAW
      TFNI = STI*RFNU*RAW
      RAZTH = 1.0D0/AZTH
      STR = ZTHR*RAZTH
      STI = -ZTHI*RAZTH
      RZTHR = STR*RAZTH*RFNU
      RZTHI = STI*RAZTH*RFNU
      ZCR = RZTHR*AR(2)
      ZCI = RZTHI*AR(2)
      RAW2 = 1.0D0/AW2
      STR = W2R*RAW2
      STI = -W2I*RAW2
      T2R = STR*RAW2
      T2I = STI*RAW2
      STR = T2R*C(2) + C(3)
      STI = T2I*C(2)
      UPR(2) = STR*TFNR - STI*TFNI
      UPI(2) = STR*TFNI + STI*TFNR
      BSUMR = UPR(2) + ZCR
      BSUMI = UPI(2) + ZCI
      ASUMR = ZEROR
      ASUMI = ZEROI
      IF (RFNU.LT.TOL) GO TO 220
      PRZTHR = RZTHR
      PRZTHI = RZTHI
      PTFNR = TFNR
      PTFNI = TFNI
      UPR(1) = CONER
      UPI(1) = CONEI
      PP = 1.0D0
      BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI))
      KS = 0
      KP1 = 2
      L = 3
      IAS = 0
      IBS = 0
      DO 210 LR=2,12,2
        LRP1 = LR + 1
C-----------------------------------------------------------------------
C     COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE TERMS IN
C     NEXT SUMA AND SUMB
C-----------------------------------------------------------------------
        DO 160 K=LR,LRP1
          KS = KS + 1
          KP1 = KP1 + 1
          L = L + 1
          ZAR = C(L)
          ZAI = ZEROI
          DO 150 J=2,KP1
            L = L + 1
            STR = ZAR*T2R - T2I*ZAI + C(L)
            ZAI = ZAR*T2I + ZAI*T2R
            ZAR = STR
  150     CONTINUE
          STR = PTFNR*TFNR - PTFNI*TFNI
          PTFNI = PTFNR*TFNI + PTFNI*TFNR
          PTFNR = STR
          UPR(KP1) = PTFNR*ZAR - PTFNI*ZAI
          UPI(KP1) = PTFNI*ZAR + PTFNR*ZAI
          CRR(KS) = PRZTHR*BR(KS+1)
          CRI(KS) = PRZTHI*BR(KS+1)
          STR = PRZTHR*RZTHR - PRZTHI*RZTHI
          PRZTHI = PRZTHR*RZTHI + PRZTHI*RZTHR
          PRZTHR = STR
          DRR(KS) = PRZTHR*AR(KS+2)
          DRI(KS) = PRZTHI*AR(KS+2)
  160   CONTINUE
        PP = PP*RFNU2
        IF (IAS.EQ.1) GO TO 180
        SUMAR = UPR(LRP1)
        SUMAI = UPI(LRP1)
        JU = LRP1
        DO 170 JR=1,LR
          JU = JU - 1
          SUMAR = SUMAR + CRR(JR)*UPR(JU) - CRI(JR)*UPI(JU)
          SUMAI = SUMAI + CRR(JR)*UPI(JU) + CRI(JR)*UPR(JU)
  170   CONTINUE
        ASUMR = ASUMR + SUMAR
        ASUMI = ASUMI + SUMAI
        TEST = DABS(SUMAR) + DABS(SUMAI)
        IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1
  180   CONTINUE
        IF (IBS.EQ.1) GO TO 200
        SUMBR = UPR(LR+2) + UPR(LRP1)*ZCR - UPI(LRP1)*ZCI
        SUMBI = UPI(LR+2) + UPR(LRP1)*ZCI + UPI(LRP1)*ZCR
        JU = LRP1
        DO 190 JR=1,LR
          JU = JU - 1
          SUMBR = SUMBR + DRR(JR)*UPR(JU) - DRI(JR)*UPI(JU)
          SUMBI = SUMBI + DRR(JR)*UPI(JU) + DRI(JR)*UPR(JU)
  190   CONTINUE
        BSUMR = BSUMR + SUMBR
        BSUMI = BSUMI + SUMBI
        TEST = DABS(SUMBR) + DABS(SUMBI)
        IF (PP.LT.BTOL .AND. TEST.LT.BTOL) IBS = 1
  200   CONTINUE
        IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 220
  210 CONTINUE
  220 CONTINUE
      ASUMR = ASUMR + CONER
      STR = -BSUMR*RFN13
      STI = -BSUMI*RFN13
      CALL ZDIV(STR, STI, RTZTR, RTZTI, BSUMR, BSUMI)
      GO TO 120
      END