# dbesj.f

          SUBROUTINE DBESJ (X, ALPHA, N, Y, NZ)
    C***BEGIN PROLOGUE  DBESJ
    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      DOUBLE 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  **** a double precision routine ****
    C         DBESJ 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 and
    C         uniform expansion are tested for underflow.  If a sequence is
    C         requested and the last member would underflow, the result is
    C         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         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      X,ALPHA are double precision
    C           X      - X .GE. 0.0D0
    C           ALPHA  - order of first member of the sequence,
    C                    ALPHA .GE. 0.0D0
    C           N      - number of members in the sequence, N .GE. 1
    C
    C         Output     Y is double precision
    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)=0.0D0, 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  D1MACH, DASYJY, DJAIRY, DLNGAM, I1MACH, XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   750101  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   900326  Removed duplicate information from DESCRIPTION section.
    C           (WRB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  DBESJ