BESK(3)

SYNOPSIS
SUBROUTINE BESK (X, FNU, KODE, N, Y, NZ)

NAME
besk - Implement forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive X and non-negative orders FNU.

LIBRARY
SLATEC

CATEGORY
C10B3

TYPE
SINGLE PRECISION (BESK-S, DBESK-D)

KEYWORDS
K BESSEL FUNCTION, SPECIAL FUNCTIONS

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract BESK implements forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions K/sub(FNU+I-1)/(X), or scaled Bessel functions EXP(X)*K/sub(FNU+I-1)/(X), I=1,...,N for real X .GT. 0.0E0 and non-negative orders FNU. If FNU .LT. NULIM, orders FNU and FNU+1 are obtained from BESKNU to start the recursion. If FNU .GE. NULIM, the uniform asymptotic expansion is used for orders FNU and FNU+1 to start the recursion. NULIM is 35 or 70 depending on whether N=1 or N .GE. 2. Under and overflow tests are made on the leading term of the asymptotic expansion before any extensive computation is done. Description of Arguments Input X - X .GT. 0.0E0 FNU - order of the initial K function, FNU .GE. 0.0E0 KODE - a parameter to indicate the scaling option KODE=1 returns Y(I)= K/sub(FNU+I-1)/(X), I=1,...,N KODE=2 returns Y(I)=EXP(X)*K/sub(FNU+I-1)/(X), I=1,...,N N - number of members in the sequence, N .GE. 1 Output y - a vector whose first n components contain values for the sequence Y(I)= K/sub(FNU+I-1)/(X), I=1,...,N or Y(I)=EXP(X)*K/sub(FNU+I-1)/(X), I=1,...,N depending on KODE NZ - number of components of Y set to zero due to underflow with KODE=1, NZ=0 , normal return, computation completed NZ .NE. 0, first NZ components of Y set to zero due to underflow, Y(I)=0.0E0, I=1,...,NZ Error Conditions Improper input arguments - a fatal error Overflow - a fatal error Underflow with KODE=1 - a non-fatal error (NZ .NE. 0)

REFERENCES
F. W. J. Olver, Tables of Bessel Functions of Moderate or Large Orders, NPL Mathematical Tables 6, Her Majesty's Stationery Office, London, 1962. N. M. Temme, On the numerical evaluation of the modified Bessel function of the third kind, Journal of Computational Physics 19, (1975), pp. 324-337.

ROUTINES CALLED
ASYIK, BESK0, BESK0E, BESK1, BESK1E, BESKNU, I1MACH, R1MACH, XERMSG

REVISION HISTORY (YYMMDD)
790201 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890531 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)