*DECK DBSKES SUBROUTINE DBSKES (XNU, X, NIN, BKE) C***BEGIN PROLOGUE DBSKES C***PURPOSE Compute a sequence of exponentially scaled modified Bessel C functions of the third kind of fractional order. C***LIBRARY SLATEC (FNLIB) C***CATEGORY C10B3 C***TYPE DOUBLE PRECISION (BESKES-S, DBSKES-D) C***KEYWORDS EXPONENTIALLY SCALED, FNLIB, FRACTIONAL ORDER, C MODIFIED BESSEL FUNCTION, SEQUENCE OF BESSEL FUNCTIONS, C SPECIAL FUNCTIONS, THIRD KIND C***AUTHOR Fullerton, W., (LANL) C***DESCRIPTION C C DBSKES(XNU,X,NIN,BKE) computes a double precision sequence C of exponentially scaled modified Bessel functions C of the third kind of order XNU + I at X, where X .GT. 0, C XNU lies in (-1,1), and I = 0, 1, ... , NIN - 1, if NIN is positive C and I = 0, -1, ... , NIN + 1, if NIN is negative. On return, the C vector BKE(.) contains the results at X for order starting at XNU. C XNU, X, and BKE are double precision. NIN is integer. C C***REFERENCES (NONE) C***ROUTINES CALLED D1MACH, D9KNUS, XERMSG C***REVISION HISTORY (YYMMDD) C 770601 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***END PROLOGUE DBSKES DOUBLE PRECISION XNU, X, BKE(*), BKNU1, V, VINCR, VEND, ALNBIG, 1 D1MACH, DIRECT SAVE ALNBIG DATA ALNBIG / 0.D0 / C***FIRST EXECUTABLE STATEMENT DBSKES IF (ALNBIG.EQ.0.D0) ALNBIG = LOG (D1MACH(2)) C V = ABS(XNU) N = ABS(NIN) C IF (V .GE. 1.D0) CALL XERMSG ('SLATEC', 'DBSKES', + 'ABS(XNU) MUST BE LT 1', 2, 2) IF (X .LE. 0.D0) CALL XERMSG ('SLATEC', 'DBSKES', 'X IS LE 0', 3, + 2) IF (N .EQ. 0) CALL XERMSG ('SLATEC', 'DBSKES', + 'N THE NUMBER IN THE SEQUENCE IS 0', 4, 2) C CALL D9KNUS (V, X, BKE(1), BKNU1, ISWTCH) IF (N.EQ.1) RETURN C VINCR = SIGN (1.0, REAL(NIN)) DIRECT = VINCR IF (XNU.NE.0.D0) DIRECT = VINCR*SIGN(1.D0, XNU) IF (ISWTCH .EQ. 1 .AND. DIRECT .GT. 0.) CALL XERMSG ('SLATEC', + 'DBSKES', 'X SO SMALL BESSEL K-SUB-XNU+1 OVERFLOWS', 5, 2) BKE(2) = BKNU1 C IF (DIRECT.LT.0.) CALL D9KNUS (ABS(XNU+VINCR), X, BKE(2), BKNU1, 1 ISWTCH) IF (N.EQ.2) RETURN C VEND = ABS (XNU+NIN) - 1.0D0 IF ((VEND-.5D0)*LOG(VEND)+0.27D0-VEND*(LOG(X)-.694D0) .GT. + ALNBIG) CALL XERMSG ('SLATEC', 'DBSKES', + 'X SO SMALL OR ABS(NU) SO BIG THAT BESSEL K-SUB-NU ' // + 'OVERFLOWS', 5, 2) C V = XNU DO 10 I=3,N V = V + VINCR BKE(I) = 2.0D0*V*BKE(I-1)/X + BKE(I-2) 10 CONTINUE C RETURN END