*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