# 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