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*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
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