DBESJ(3)

SYNOPSIS
SUBROUTINE DBESJ (X, ALPHA, N, Y, NZ)

NAME
dbesj - Compute an N member sequence of J Bessel functions J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA and X.

LIBRARY
SLATEC

CATEGORY
C10A3

TYPE
DOUBLE PRECISION (BESJ-S, DBESJ-D)

KEYWORDS
J BESSEL FUNCTION, SPECIAL FUNCTIONS

AUTHOR
Amos, D. E., (SNLA) Daniel, S. L., (SNLA) Weston, M. K., (SNLA)

DESCRIPTION
Abstract **** a double precision routine **** DBESJ computes an N member sequence of J Bessel functions J/sub(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA and X. A combination of the power series, the asymptotic expansion for X to infinity and the uniform asymptotic expansion for NU to infinity are applied over subdivisions of the (NU,X) plane. For values of (NU,X) not covered by one of these formulae, the order is incremented or decremented by integer values into a region where one of the formulae apply. Backward recursion is applied to reduce orders by integer values except where the entire sequence lies in the oscillatory region. In this case forward recursion is stable and values from the asymptotic expansion for X to infinity start the recursion when it is efficient to do so. Leading terms of the series and uniform expansion are tested for underflow. If a sequence is requested and the last member would underflow, the result is set to zero and the next lower order tried, etc., until a member comes on scale or all members are set to zero. Overflow cannot occur. The maximum number of significant digits obtainable is the smaller of 14 and the number of digits carried in double precision arithmetic. Description of Arguments Input X,ALPHA are double precision X - X .GE. 0.0D0 ALPHA - order of first member of the sequence, ALPHA .GE. 0.0D0 N - number of members in the sequence, N .GE. 1 Output Y is double precision Y - a vector whose first N components contain values for J/sub(ALPHA+K-1)/(X), K=1,...,N NZ - number of components of Y set to zero due to underflow, NZ=0 , normal return, computation completed NZ .NE. 0, last NZ components of Y set to zero, Y(K)=0.0D0, K=N-NZ+1,...,N. Error Conditions Improper input arguments - a fatal error Underflow - a non-fatal error (NZ .NE. 0)

REFERENCES
D. E. Amos, S. L. Daniel and M. K. Weston, CDC 6600 subroutines IBESS and JBESS for Bessel functions I(NU,X) and J(NU,X), X .GE. 0, NU .GE. 0, ACM Transactions on Mathematical Software 3, (1977), pp. 76-92. F. W. J. Olver, Tables of Bessel Functions of Moderate or Large Orders, NPL Mathematical Tables 6, Her Majesty's Stationery Office, London, 1962.

ROUTINES CALLED
D1MACH, DASYJY, DJAIRY, DLNGAM, I1MACH, XERMSG

REVISION HISTORY (YYMMDD)
750101 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890911 Removed unnecessary intrinsics. (WRB)
890911 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)