BESY(3)

SYNOPSIS
SUBROUTINE BESY (X, FNU, N, Y)

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

LIBRARY
SLATEC

CATEGORY
C10A3

TYPE
SINGLE PRECISION (BESY-S, DBESY-D)

KEYWORDS
SPECIAL FUNCTIONS, Y BESSEL FUNCTION

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract BESY implements forward recursion on the three term recursion relation for a sequence of non-negative order Bessel functions Y/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 BESYNU which computes by a power series for X .LE. 2, the K Bessel function of an imaginary argument for 2 .LT. X .LE. 20 and the asymptotic expansion for X .GT. 20. If FNU .GE. NULIM, the uniform asymptotic expansion is coded in ASYJY for orders FNU and FNU+1 to start the recursion. NULIM is 70 or 100 depending on whether N=1 or N .GE. 2. An overflow test is 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 Y function, FNU .GE. 0.0E0 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)=Y/sub(FNU+I-1)/(X), I=1,N. Error Conditions Improper input arguments - a fatal error Overflow - a fatal error

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. N. M. Temme, On the numerical evaluation of the ordinary Bessel function of the second kind, Journal of Computational Physics 21, (1976), pp. 343-350.

ROUTINES CALLED
ASYJY, BESY0, BESY1, BESYNU, I1MACH, R1MACH, XERMSG, YAIRY

REVISION HISTORY (YYMMDD)
800501 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)