715 lines
34 KiB
Fortran
715 lines
34 KiB
Fortran
SUBROUTINE ZUNHJ(ZR, ZI, FNU, IPMTR, TOL, PHIR, PHII, ARGR, ARGI,
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* ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
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C***BEGIN PROLOGUE ZUNHJ
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C***REFER TO ZBESI,ZBESK
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C
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C REFERENCES
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C HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A.
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C STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9.
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C
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C ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC
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C PRESS, N.Y., 1974, PAGE 420
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C
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C ABSTRACT
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C ZUNHJ COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) =
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C J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU
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C BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION
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C
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C C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) )
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C
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C FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS
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C AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE.
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C
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C (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2,
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C
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C ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING
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C PURPOSES IN AIRY FUNCTIONS FROM CAIRY OR CBIRY.
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C
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C MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND
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C MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR=
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C 1 COMPUTES ALL EXCEPT ASUM AND BSUM.
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C
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C***ROUTINES CALLED AZABS,ZDIV,AZLOG,AZSQRT,D1MACH
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C***END PROLOGUE ZUNHJ
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C COMPLEX ARG,ASUM,BSUM,CFNU,CONE,CR,CZERO,DR,P,PHI,PRZTH,PTFN,
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C *RFN13,RTZTA,RZTH,SUMA,SUMB,TFN,T2,UP,W,W2,Z,ZA,ZB,ZC,ZETA,ZETA1,
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C *ZETA2,ZTH
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DOUBLE PRECISION ALFA, ANG, AP, AR, ARGI, ARGR, ASUMI, ASUMR,
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* ATOL, AW2, AZTH, BETA, BR, BSUMI, BSUMR, BTOL, C, CONEI, CONER,
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* CRI, CRR, DRI, DRR, EX1, EX2, FNU, FN13, FN23, GAMA, GPI, HPI,
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* PHII, PHIR, PI, PP, PR, PRZTHI, PRZTHR, PTFNI, PTFNR, RAW, RAW2,
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* RAZTH, RFNU, RFNU2, RFN13, RTZTI, RTZTR, RZTHI, RZTHR, STI, STR,
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* SUMAI, SUMAR, SUMBI, SUMBR, TEST, TFNI, TFNR, THPI, TOL, TZAI,
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* TZAR, T2I, T2R, UPI, UPR, WI, WR, W2I, W2R, ZAI, ZAR, ZBI, ZBR,
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* ZCI, ZCR, ZEROI, ZEROR, ZETAI, ZETAR, ZETA1I, ZETA1R, ZETA2I,
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* ZETA2R, ZI, ZR, ZTHI, ZTHR, AZABS, AC, D1MACH
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INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR,
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* LRP1, L1, L2, M, IDUM
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DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30),
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* AP(30), PR(30), PI(30), UPR(14), UPI(14), CRR(14), CRI(14),
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* DRR(14), DRI(14)
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DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7), AR(8),
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1 AR(9), AR(10), AR(11), AR(12), AR(13), AR(14)/
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2 1.00000000000000000D+00, 1.04166666666666667D-01,
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3 8.35503472222222222D-02, 1.28226574556327160D-01,
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4 2.91849026464140464D-01, 8.81627267443757652D-01,
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5 3.32140828186276754D+00, 1.49957629868625547D+01,
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6 7.89230130115865181D+01, 4.74451538868264323D+02,
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7 3.20749009089066193D+03, 2.40865496408740049D+04,
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8 1.98923119169509794D+05, 1.79190200777534383D+06/
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DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7), BR(8),
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1 BR(9), BR(10), BR(11), BR(12), BR(13), BR(14)/
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2 1.00000000000000000D+00, -1.45833333333333333D-01,
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3 -9.87413194444444444D-02, -1.43312053915895062D-01,
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4 -3.17227202678413548D-01, -9.42429147957120249D-01,
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5 -3.51120304082635426D+00, -1.57272636203680451D+01,
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6 -8.22814390971859444D+01, -4.92355370523670524D+02,
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7 -3.31621856854797251D+03, -2.48276742452085896D+04,
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8 -2.04526587315129788D+05, -1.83844491706820990D+06/
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DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10),
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1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18),
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2 C(19), C(20), C(21), C(22), C(23), C(24)/
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3 1.00000000000000000D+00, -2.08333333333333333D-01,
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4 1.25000000000000000D-01, 3.34201388888888889D-01,
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5 -4.01041666666666667D-01, 7.03125000000000000D-02,
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6 -1.02581259645061728D+00, 1.84646267361111111D+00,
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7 -8.91210937500000000D-01, 7.32421875000000000D-02,
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8 4.66958442342624743D+00, -1.12070026162229938D+01,
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9 8.78912353515625000D+00, -2.36408691406250000D+00,
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A 1.12152099609375000D-01, -2.82120725582002449D+01,
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B 8.46362176746007346D+01, -9.18182415432400174D+01,
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C 4.25349987453884549D+01, -7.36879435947963170D+00,
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D 2.27108001708984375D-01, 2.12570130039217123D+02,
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E -7.65252468141181642D+02, 1.05999045252799988D+03/
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DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32),
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1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40),
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2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/
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3 -6.99579627376132541D+02, 2.18190511744211590D+02,
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4 -2.64914304869515555D+01, 5.72501420974731445D-01,
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5 -1.91945766231840700D+03, 8.06172218173730938D+03,
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6 -1.35865500064341374D+04, 1.16553933368645332D+04,
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7 -5.30564697861340311D+03, 1.20090291321635246D+03,
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8 -1.08090919788394656D+02, 1.72772750258445740D+00,
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9 2.02042913309661486D+04, -9.69805983886375135D+04,
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A 1.92547001232531532D+05, -2.03400177280415534D+05,
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B 1.22200464983017460D+05, -4.11926549688975513D+04,
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C 7.10951430248936372D+03, -4.93915304773088012D+02,
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D 6.07404200127348304D+00, -2.42919187900551333D+05,
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E 1.31176361466297720D+06, -2.99801591853810675D+06/
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DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56),
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1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64),
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2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/
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3 3.76327129765640400D+06, -2.81356322658653411D+06,
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4 1.26836527332162478D+06, -3.31645172484563578D+05,
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5 4.52187689813627263D+04, -2.49983048181120962D+03,
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6 2.43805296995560639D+01, 3.28446985307203782D+06,
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7 -1.97068191184322269D+07, 5.09526024926646422D+07,
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8 -7.41051482115326577D+07, 6.63445122747290267D+07,
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9 -3.75671766607633513D+07, 1.32887671664218183D+07,
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A -2.78561812808645469D+06, 3.08186404612662398D+05,
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B -1.38860897537170405D+04, 1.10017140269246738D+02,
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C -4.93292536645099620D+07, 3.25573074185765749D+08,
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D -9.39462359681578403D+08, 1.55359689957058006D+09,
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E -1.62108055210833708D+09, 1.10684281682301447D+09/
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DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80),
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1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88),
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2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/
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3 -4.95889784275030309D+08, 1.42062907797533095D+08,
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4 -2.44740627257387285D+07, 2.24376817792244943D+06,
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5 -8.40054336030240853D+04, 5.51335896122020586D+02,
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6 8.14789096118312115D+08, -5.86648149205184723D+09,
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7 1.86882075092958249D+10, -3.46320433881587779D+10,
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8 4.12801855797539740D+10, -3.30265997498007231D+10,
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9 1.79542137311556001D+10, -6.56329379261928433D+09,
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A 1.55927986487925751D+09, -2.25105661889415278D+08,
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B 1.73951075539781645D+07, -5.49842327572288687D+05,
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C 3.03809051092238427D+03, -1.46792612476956167D+10,
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D 1.14498237732025810D+11, -3.99096175224466498D+11,
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E 8.19218669548577329D+11, -1.09837515608122331D+12/
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DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104),
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1 C(105)/
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2 1.00815810686538209D+12, -6.45364869245376503D+11,
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3 2.87900649906150589D+11, -8.78670721780232657D+10,
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4 1.76347306068349694D+10, -2.16716498322379509D+09,
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5 1.43157876718888981D+08, -3.87183344257261262D+06,
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6 1.82577554742931747D+04/
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DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5), ALFA(6),
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1 ALFA(7), ALFA(8), ALFA(9), ALFA(10), ALFA(11), ALFA(12),
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2 ALFA(13), ALFA(14), ALFA(15), ALFA(16), ALFA(17), ALFA(18),
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3 ALFA(19), ALFA(20), ALFA(21), ALFA(22)/
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4 -4.44444444444444444D-03, -9.22077922077922078D-04,
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5 -8.84892884892884893D-05, 1.65927687832449737D-04,
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6 2.46691372741792910D-04, 2.65995589346254780D-04,
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7 2.61824297061500945D-04, 2.48730437344655609D-04,
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8 2.32721040083232098D-04, 2.16362485712365082D-04,
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9 2.00738858762752355D-04, 1.86267636637545172D-04,
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A 1.73060775917876493D-04, 1.61091705929015752D-04,
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B 1.50274774160908134D-04, 1.40503497391269794D-04,
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C 1.31668816545922806D-04, 1.23667445598253261D-04,
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D 1.16405271474737902D-04, 1.09798298372713369D-04,
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E 1.03772410422992823D-04, 9.82626078369363448D-05/
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DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26), ALFA(27), ALFA(28),
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1 ALFA(29), ALFA(30), ALFA(31), ALFA(32), ALFA(33), ALFA(34),
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2 ALFA(35), ALFA(36), ALFA(37), ALFA(38), ALFA(39), ALFA(40),
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3 ALFA(41), ALFA(42), ALFA(43), ALFA(44)/
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4 9.32120517249503256D-05, 8.85710852478711718D-05,
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5 8.42963105715700223D-05, 8.03497548407791151D-05,
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6 7.66981345359207388D-05, 7.33122157481777809D-05,
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7 7.01662625163141333D-05, 6.72375633790160292D-05,
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8 6.93735541354588974D-04, 2.32241745182921654D-04,
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9 -1.41986273556691197D-05, -1.16444931672048640D-04,
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A -1.50803558053048762D-04, -1.55121924918096223D-04,
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B -1.46809756646465549D-04, -1.33815503867491367D-04,
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C -1.19744975684254051D-04, -1.06184319207974020D-04,
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D -9.37699549891194492D-05, -8.26923045588193274D-05,
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E -7.29374348155221211D-05, -6.44042357721016283D-05/
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DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48), ALFA(49), ALFA(50),
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1 ALFA(51), ALFA(52), ALFA(53), ALFA(54), ALFA(55), ALFA(56),
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2 ALFA(57), ALFA(58), ALFA(59), ALFA(60), ALFA(61), ALFA(62),
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3 ALFA(63), ALFA(64), ALFA(65), ALFA(66)/
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4 -5.69611566009369048D-05, -5.04731044303561628D-05,
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5 -4.48134868008882786D-05, -3.98688727717598864D-05,
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6 -3.55400532972042498D-05, -3.17414256609022480D-05,
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7 -2.83996793904174811D-05, -2.54522720634870566D-05,
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8 -2.28459297164724555D-05, -2.05352753106480604D-05,
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9 -1.84816217627666085D-05, -1.66519330021393806D-05,
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A -1.50179412980119482D-05, -1.35554031379040526D-05,
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B -1.22434746473858131D-05, -1.10641884811308169D-05,
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C -3.54211971457743841D-04, -1.56161263945159416D-04,
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D 3.04465503594936410D-05, 1.30198655773242693D-04,
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E 1.67471106699712269D-04, 1.70222587683592569D-04/
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DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70), ALFA(71), ALFA(72),
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1 ALFA(73), ALFA(74), ALFA(75), ALFA(76), ALFA(77), ALFA(78),
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2 ALFA(79), ALFA(80), ALFA(81), ALFA(82), ALFA(83), ALFA(84),
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3 ALFA(85), ALFA(86), ALFA(87), ALFA(88)/
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4 1.56501427608594704D-04, 1.36339170977445120D-04,
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5 1.14886692029825128D-04, 9.45869093034688111D-05,
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6 7.64498419250898258D-05, 6.07570334965197354D-05,
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7 4.74394299290508799D-05, 3.62757512005344297D-05,
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8 2.69939714979224901D-05, 1.93210938247939253D-05,
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9 1.30056674793963203D-05, 7.82620866744496661D-06,
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A 3.59257485819351583D-06, 1.44040049814251817D-07,
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B -2.65396769697939116D-06, -4.91346867098485910D-06,
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C -6.72739296091248287D-06, -8.17269379678657923D-06,
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D -9.31304715093561232D-06, -1.02011418798016441D-05,
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E -1.08805962510592880D-05, -1.13875481509603555D-05/
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DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92), ALFA(93), ALFA(94),
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1 ALFA(95), ALFA(96), ALFA(97), ALFA(98), ALFA(99), ALFA(100),
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2 ALFA(101), ALFA(102), ALFA(103), ALFA(104), ALFA(105),
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3 ALFA(106), ALFA(107), ALFA(108), ALFA(109), ALFA(110)/
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4 -1.17519675674556414D-05, -1.19987364870944141D-05,
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5 3.78194199201772914D-04, 2.02471952761816167D-04,
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6 -6.37938506318862408D-05, -2.38598230603005903D-04,
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7 -3.10916256027361568D-04, -3.13680115247576316D-04,
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8 -2.78950273791323387D-04, -2.28564082619141374D-04,
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9 -1.75245280340846749D-04, -1.25544063060690348D-04,
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A -8.22982872820208365D-05, -4.62860730588116458D-05,
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B -1.72334302366962267D-05, 5.60690482304602267D-06,
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C 2.31395443148286800D-05, 3.62642745856793957D-05,
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D 4.58006124490188752D-05, 5.24595294959114050D-05,
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E 5.68396208545815266D-05, 5.94349820393104052D-05/
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DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114), ALFA(115),
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1 ALFA(116), ALFA(117), ALFA(118), ALFA(119), ALFA(120),
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2 ALFA(121), ALFA(122), ALFA(123), ALFA(124), ALFA(125),
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3 ALFA(126), ALFA(127), ALFA(128), ALFA(129), ALFA(130)/
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4 6.06478527578421742D-05, 6.08023907788436497D-05,
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5 6.01577894539460388D-05, 5.89199657344698500D-05,
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6 5.72515823777593053D-05, 5.52804375585852577D-05,
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7 5.31063773802880170D-05, 5.08069302012325706D-05,
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8 4.84418647620094842D-05, 4.60568581607475370D-05,
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9 -6.91141397288294174D-04, -4.29976633058871912D-04,
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A 1.83067735980039018D-04, 6.60088147542014144D-04,
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B 8.75964969951185931D-04, 8.77335235958235514D-04,
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C 7.49369585378990637D-04, 5.63832329756980918D-04,
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D 3.68059319971443156D-04, 1.88464535514455599D-04/
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DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134), ALFA(135),
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1 ALFA(136), ALFA(137), ALFA(138), ALFA(139), ALFA(140),
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2 ALFA(141), ALFA(142), ALFA(143), ALFA(144), ALFA(145),
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3 ALFA(146), ALFA(147), ALFA(148), ALFA(149), ALFA(150)/
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4 3.70663057664904149D-05, -8.28520220232137023D-05,
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5 -1.72751952869172998D-04, -2.36314873605872983D-04,
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6 -2.77966150694906658D-04, -3.02079514155456919D-04,
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7 -3.12594712643820127D-04, -3.12872558758067163D-04,
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8 -3.05678038466324377D-04, -2.93226470614557331D-04,
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|
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 = AZABS(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 AZSQRT(SUMAR, SUMAI, ZAR, ZAI)
|
|
CALL AZSQRT(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 AZSQRT(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 AZSQRT(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 AZLOG(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 = AZABS(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 AZSQRT(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
|