besj.f
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