# SLATEC Routines --- BESJ ---

```*DECK BESJ
SUBROUTINE BESJ (X, ALPHA, N, Y, NZ)
C***BEGIN PROLOGUE  BESJ
C***PURPOSE  Compute an N member sequence of J Bessel functions
C            J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA
C            and X.
C***LIBRARY   SLATEC
C***CATEGORY  C10A3
C***TYPE      SINGLE PRECISION (BESJ-S, DBESJ-D)
C***KEYWORDS  J BESSEL FUNCTION, SPECIAL FUNCTIONS
C***AUTHOR  Amos, D. E., (SNLA)
C           Daniel, S. L., (SNLA)
C           Weston, M. K., (SNLA)
C***DESCRIPTION
C
C     Abstract
C         BESJ computes an N member sequence of J Bessel functions
C         J/sub(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA and X.
C         A combination of the power series, the asymptotic expansion
C         for X to infinity and the uniform asymptotic expansion for
C         NU to infinity are applied over subdivisions of the (NU,X)
C         plane.  For values of (NU,X) not covered by one of these
C         formulae, the order is incremented or decremented by integer
C         values into a region where one of the formulae apply. Backward
C         recursion is applied to reduce orders by integer values except
C         where the entire sequence lies in the oscillatory region.  In
C         this case forward recursion is stable and values from the
C         asymptotic expansion for X to infinity start the recursion
C         when it is efficient to do so.  Leading terms of the series
C         and uniform expansion are tested for underflow.  If a sequence
C         is requested and the last member would underflow, the result
C         is set to zero and the next lower order tried, etc., until a
C         member comes on scale or all members are set to zero.
C         Overflow cannot occur.
C
C     Description of Arguments
C
C         Input
C           X      - X .GE. 0.0E0
C           ALPHA  - order of first member of the sequence,
C                    ALPHA .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
C                    values for J/sub(ALPHA+K-1)/(X), K=1,...,N
C           NZ     - number of components of Y set to zero due to
C                    underflow,
C                    NZ=0   , normal return, computation completed
C                    NZ .NE. 0, last NZ components of Y set to zero,
C                             Y(K)=0.0E0, K=N-NZ+1,...,N.
C
C     Error Conditions
C         Improper input arguments - a fatal error
C         Underflow  - a non-fatal error (NZ .NE. 0)
C
C***REFERENCES  D. E. Amos, S. L. Daniel and M. K. Weston, CDC 6600
C                 subroutines IBESS and JBESS for Bessel functions
C                 I(NU,X) and J(NU,X), X .GE. 0, NU .GE. 0, ACM
C                 Transactions on Mathematical Software 3, (1977),
C                 pp. 76-92.
C               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***ROUTINES CALLED  ALNGAM, ASYJY, I1MACH, JAIRY, R1MACH, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   750101  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  BESJ
```