besy.f
SUBROUTINE BESY (X, FNU, N, Y)
C***BEGIN PROLOGUE BESY
C***PURPOSE Implement forward recursion on the three term recursion
C relation for a sequence of non-negative order Bessel
C functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
C X and non-negative orders FNU.
C***LIBRARY SLATEC
C***CATEGORY C10A3
C***TYPE SINGLE PRECISION (BESY-S, DBESY-D)
C***KEYWORDS SPECIAL FUNCTIONS, Y BESSEL FUNCTION
C***AUTHOR Amos, D. E., (SNLA)
C***DESCRIPTION
C
C Abstract
C BESY implements forward recursion on the three term
C recursion relation for a sequence of non-negative order Bessel
C functions Y/sub(FNU+I-1)/(X), I=1,N for real X .GT. 0.0E0 and
C non-negative orders FNU. If FNU .LT. NULIM, orders FNU and
C FNU+1 are obtained from BESYNU which computes by a power
C series for X .LE. 2, the K Bessel function of an imaginary
C argument for 2 .LT. X .LE. 20 and the asymptotic expansion for
C X .GT. 20.
C
C If FNU .GE. NULIM, the uniform asymptotic expansion is coded
C in ASYJY for orders FNU and FNU+1 to start the recursion.
C NULIM is 70 or 100 depending on whether N=1 or N .GE. 2. An
C overflow test is made on the leading term of the asymptotic
C expansion before any extensive computation is done.
C
C Description of Arguments
C
C Input
C X - X .GT. 0.0E0
C FNU - order of the initial Y function, FNU .GE. 0.0E0
C N - number of members in the sequence, N .GE. 1
C
C Output
C Y - a vector whose first N components contain values
C for the sequence Y(I)=Y/sub(FNU+I-1)/(X), I=1,N.
C
C Error Conditions
C Improper input arguments - a fatal error
C Overflow - a fatal error
C
C***REFERENCES F. W. J. Olver, Tables of Bessel Functions of Moderate
C or Large Orders, NPL Mathematical Tables 6, Her
C Majesty's Stationery Office, London, 1962.
C N. M. Temme, On the numerical evaluation of the modified
C Bessel function of the third kind, Journal of
C Computational Physics 19, (1975), pp. 324-337.
C N. M. Temme, On the numerical evaluation of the ordinary
C Bessel function of the second kind, Journal of
C Computational Physics 21, (1976), pp. 343-350.
C***ROUTINES CALLED ASYJY, BESY0, BESY1, BESYNU, I1MACH, R1MACH,
C XERMSG, YAIRY
C***REVISION HISTORY (YYMMDD)
C 800501 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 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 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE BESY