 
      SUBROUTINE BESY(X,FNU,N,Y)
C***BEGIN PROLOGUE  BESY
C***DATE WRITTEN   800501   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  C10A3
C***KEYWORDS  BESSEL FUNCTION,SPECIAL FUNCTION,Y BESSEL FUNCTION
C***AUTHOR  AMOS, D. E., (Sandia National Laboratories, Albuquerque)
C***PURPOSE  BESY implements forward recursion on the three term recur-
C            sion 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.
C***DESCRIPTION
C
C     Written by D. E. Amos, May, 1980
C
C     References
C         SAND-80-1498
C
C         On the Numerical Evaluation of the Ordinary Bessel Function
C         of the Second Kind by N. M. Temme, J. Comp. Physics, 21,
C         1976, pp. 343-350.
C
C         On the Numerical Evaluation of the Modified Bessel Function
C         of the Third Kind by N. M. Temme, J. Comp. Physics, 19, 1975,
C         pp. 324-337.
C
C         Tables of Bessel Functions of Moderate or Large Orders,
C         NPL Mathematical Tables, Vol. 6, by F. W. J. Olver, Her
C         Majesty's Stationery Office, London, 1962.
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         BESY calls BESYNU,GAMMA,ASYJY,SIH,COSH,BESY0,BESY1
C                    I1MACH,R1MACH,XERROR
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***REFERENCES  (NONE)
C***ROUTINES CALLED  ASYJY,BESY0,BESY1,BESYNU,I1MACH,R1MACH,XERROR,
C                    YAIRY
C***END PROLOGUE  BESY
C
 
 
