*DECK D9GMIC DOUBLE PRECISION FUNCTION D9GMIC (A, X, ALX) C***BEGIN PROLOGUE D9GMIC C***SUBSIDIARY C***PURPOSE Compute the complementary incomplete Gamma function for A C near a negative integer and X small. C***LIBRARY SLATEC (FNLIB) C***CATEGORY C7E C***TYPE DOUBLE PRECISION (R9GMIC-S, D9GMIC-D) C***KEYWORDS COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB, SMALL X, C SPECIAL FUNCTIONS C***AUTHOR Fullerton, W., (LANL) C***DESCRIPTION C C Compute the complementary incomplete gamma function for A near C a negative integer and for small X. C C***REFERENCES (NONE) C***ROUTINES CALLED D1MACH, DLNGAM, XERMSG C***REVISION HISTORY (YYMMDD) C 770701 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) C 890911 Removed unnecessary intrinsics. (WRB) C 890911 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) C 900720 Routine changed from user-callable to subsidiary. (WRB) C***END PROLOGUE D9GMIC DOUBLE PRECISION A, X, ALX, ALNG, BOT, EPS, EULER, FK, FKP1, FM, 1 S, SGNG, T, TE, D1MACH, DLNGAM LOGICAL FIRST SAVE EULER, EPS, BOT, FIRST DATA EULER / 0.5772156649 0153286060 6512090082 40 D0 / DATA FIRST /.TRUE./ C***FIRST EXECUTABLE STATEMENT D9GMIC IF (FIRST) THEN EPS = 0.5D0*D1MACH(3) BOT = LOG (D1MACH(1)) ENDIF FIRST = .FALSE. C IF (A .GT. 0.D0) CALL XERMSG ('SLATEC', 'D9GMIC', + 'A MUST BE NEAR A NEGATIVE INTEGER', 2, 2) IF (X .LE. 0.D0) CALL XERMSG ('SLATEC', 'D9GMIC', + 'X MUST BE GT ZERO', 3, 2) C M = -(A - 0.5D0) FM = M C TE = 1.0D0 T = 1.0D0 S = T DO 20 K=1,200 FKP1 = K + 1 TE = -X*TE/(FM+FKP1) T = TE/FKP1 S = S + T IF (ABS(T).LT.EPS*S) GO TO 30 20 CONTINUE CALL XERMSG ('SLATEC', 'D9GMIC', + 'NO CONVERGENCE IN 200 TERMS OF CONTINUED FRACTION', 4, 2) C 30 D9GMIC = -ALX - EULER + X*S/(FM+1.0D0) IF (M.EQ.0) RETURN C IF (M.EQ.1) D9GMIC = -D9GMIC - 1.D0 + 1.D0/X IF (M.EQ.1) RETURN C TE = FM T = 1.D0 S = T MM1 = M - 1 DO 40 K=1,MM1 FK = K TE = -X*TE/FK T = TE/(FM-FK) S = S + T IF (ABS(T).LT.EPS*ABS(S)) GO TO 50 40 CONTINUE C 50 DO 60 K=1,M D9GMIC = D9GMIC + 1.0D0/K 60 CONTINUE C SGNG = 1.0D0 IF (MOD(M,2).EQ.1) SGNG = -1.0D0 ALNG = LOG(D9GMIC) - DLNGAM(FM+1.D0) C D9GMIC = 0.D0 IF (ALNG.GT.BOT) D9GMIC = SGNG * EXP(ALNG) IF (S.NE.0.D0) D9GMIC = D9GMIC + 1 SIGN (EXP(-FM*ALX+LOG(ABS(S)/FM)), S) C IF (D9GMIC .EQ. 0.D0 .AND. S .EQ. 0.D0) CALL XERMSG ('SLATEC', + 'D9GMIC', 'RESULT UNDERFLOWS', 1, 1) RETURN C END