SLATEC Routines --- DBESY ---

```*DECK DBESY
SUBROUTINE DBESY (X, FNU, N, Y)
C***BEGIN PROLOGUE  DBESY
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      DOUBLE PRECISION (BESY-S, DBESY-D)
C***KEYWORDS  SPECIAL FUNCTIONS, Y BESSEL FUNCTION
C***AUTHOR  Amos, D. E., (SNLA)
C***DESCRIPTION
C
C     Abstract  **** a double precision routine ****
C         DBESY 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. 0.0D0 and
C         non-negative orders FNU.  If FNU .LT. NULIM, orders FNU and
C         FNU+1 are obtained from DBSYNU 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 DASYJY 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         The maximum number of significant digits obtainable
C         is the smaller of 14 and the number of digits carried in
C         double precision arithmetic.
C
C     Description of Arguments
C
C         Input
C           X      - X .GT. 0.0D0
C           FNU    - order of the initial Y function, FNU .GE. 0.0D0
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  D1MACH, DASYJY, DBESY0, DBESY1, DBSYNU, DYAIRY,
C                    I1MACH, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   800501  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890911  Removed unnecessary intrinsics.  (WRB)
C   890911  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   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DBESY
```