SLATEC Routines --- BESK ---

```*DECK BESK
SUBROUTINE BESK (X, FNU, KODE, N, Y, NZ)
C***BEGIN PROLOGUE  BESK
C***PURPOSE  Implement forward recursion on the three term recursion
C            relation for a sequence of non-negative order Bessel
C            functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions
C            EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
C            X and non-negative orders FNU.
C***LIBRARY   SLATEC
C***CATEGORY  C10B3
C***TYPE      SINGLE PRECISION (BESK-S, DBESK-D)
C***KEYWORDS  K BESSEL FUNCTION, SPECIAL FUNCTIONS
C***AUTHOR  Amos, D. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C         BESK implements forward recursion on the three term
C         recursion relation for a sequence of non-negative order Bessel
C         functions K/sub(FNU+I-1)/(X), or scaled Bessel functions
C         EXP(X)*K/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 BESKNU to start the recursion.  If
C         FNU .GE. NULIM, the uniform asymptotic expansion is used for
C         orders FNU and FNU+1 to start the recursion.  NULIM is 35 or
C         70 depending on whether N=1 or N .GE. 2.  Under and overflow
C         tests are made on the leading term of the asymptotic expansion
C         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 K function, FNU .GE. 0.0E0
C           KODE   - a parameter to indicate the scaling option
C                    KODE=1 returns Y(I)=       K/sub(FNU+I-1)/(X),
C                                        I=1,...,N
C                    KODE=2 returns Y(I)=EXP(X)*K/sub(FNU+I-1)/(X),
C                                        I=1,...,N
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
C                    Y(I)=       K/sub(FNU+I-1)/(X), I=1,...,N  or
C                    Y(I)=EXP(X)*K/sub(FNU+I-1)/(X), I=1,...,N
C                    depending on KODE
C           NZ     - number of components of Y set to zero due to
C                    underflow with KODE=1,
C                    NZ=0   , normal return, computation completed
C                    NZ .NE. 0, first NZ components of Y set to zero
C                             due to underflow, Y(I)=0.0E0, I=1,...,NZ
C
C     Error Conditions
C         Improper input arguments - a fatal error
C         Overflow - a fatal error
C         Underflow with KODE=1 -  a non-fatal error (NZ .NE. 0)
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***ROUTINES CALLED  ASYIK, BESK0, BESK0E, BESK1, BESK1E, BESKNU,
C                    I1MACH, R1MACH, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   790201  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  BESK
```