SLATEC Routines --- DBSKIN ---
*DECK DBSKIN
SUBROUTINE DBSKIN (X, N, KODE, M, Y, NZ, IERR)
C***BEGIN PROLOGUE DBSKIN
C***PURPOSE Compute repeated integrals of the K-zero Bessel function.
C***LIBRARY SLATEC
C***CATEGORY C10F
C***TYPE DOUBLE PRECISION (BSKIN-S, DBSKIN-D)
C***KEYWORDS BICKLEY FUNCTIONS, EXPONENTIAL INTEGRAL,
C INTEGRALS OF BESSEL FUNCTIONS, K-ZERO BESSEL FUNCTION
C***AUTHOR Amos, D. E., (SNLA)
C***DESCRIPTION
C
C The following definitions are used in DBSKIN:
C
C Definition 1
C KI(0,X) = K-zero Bessel function.
C
C Definition 2
C KI(N,X) = Bickley Function
C = integral from X to infinity of KI(N-1,t)dt
C for X .ge. 0 and N = 1,2,...
C _____________________________________________________________________
C DBSKIN computes a sequence of Bickley functions (repeated integrals
C of the K0 Bessel function); i.e. for fixed X and N and for K=1,...,
C DBSKIN computes the sequence
C
C Y(K) = KI(N+K-1,X) for KODE=1
C or
C Y(K) = EXP(X)*KI(N+K-1,X) for KODE=2,
C
C for N.ge.0 and X.ge.0 (N and X cannot be zero simultaneously).
C
C INPUT X is DOUBLE PRECISION
C X - Argument, X .ge. 0.0D0
C N - Order of first member of the sequence N .ge. 0
C KODE - Selection parameter
C KODE = 1 returns Y(K)= KI(N+K-1,X), K=1,M
C = 2 returns Y(K)=EXP(X)*KI(N+K-1,X), K=1,M
C M - Number of members in the sequence, M.ge.1
C
C OUTPUT Y is a DOUBLE PRECISION VECTOR
C Y - A vector of dimension at least M containing the
C sequence selected by KODE.
C NZ - Underflow flag
C NZ = 0 means computation completed
C = 1 means an exponential underflow occurred on
C KODE=1. Y(K)=0.0D0, K=1,...,M is returned
C KODE=1 AND Y(K)=0.0E0, K=1,...,M IS RETURNED
C IERR - Error flag
C IERR=0, Normal return, computation completed
C IERR=1, Input error, no computation
C IERR=2, Error, no computation
C Algorithm termination condition not met
C
C The nominal computational accuracy is the maximum of unit
C roundoff (=D1MACH(4)) and 1.0D-18 since critical constants
C are given to only 18 digits.
C
C BSKIN is the single precision version of DBSKIN.
C
C *Long Description:
C
C Numerical recurrence on
C
C (L-1)*KI(L,X) = X(KI(L-3,X) - KI(L-1,X)) + (L-2)*KI(L-2,X)
C
C is stable where recurrence is carried forward or backward
C away from INT(X+0.5). The power series for indices 0,1 and 2
C on 0.le.X.le.2 starts a stable recurrence for indices
C greater than 2. If N is sufficiently large (N.gt.NLIM), the
C uniform asymptotic expansion for N to INFINITY is more
C economical. On X.gt.2 the recursion is started by evaluating
C the uniform expansion for the three members whose indices are
C closest to INT(X+0.5) within the set N,...,N+M-1. Forward
C recurrence, backward recurrence or both complete the
C sequence depending on the relation of INT(X+0.5) to the
C indices N,...,N+M-1.
C
C***REFERENCES D. E. Amos, Uniform asymptotic expansions for
C exponential integrals E(N,X) and Bickley functions
C KI(N,X), ACM Transactions on Mathematical Software,
C 1983.
C D. E. Amos, A portable Fortran subroutine for the
C Bickley functions KI(N,X), Algorithm 609, ACM
C Transactions on Mathematical Software, 1983.
C***ROUTINES CALLED D1MACH, DBKIAS, DBKISR, DEXINT, DGAMRN, I1MACH
C***REVISION HISTORY (YYMMDD)
C 820601 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890911 Removed unnecessary intrinsics. (WRB)
C 891006 Cosmetic changes to prologue. (WRB)
C 891009 Removed unreferenced statement label. (WRB)
C 891009 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE DBSKIN