*DECK DBESI SUBROUTINE DBESI (X, ALPHA, KODE, N, Y, NZ) C***BEGIN PROLOGUE DBESI C***PURPOSE Compute an N member sequence of I Bessel functions C I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions C EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for nonnegative C ALPHA and X. C***LIBRARY SLATEC C***CATEGORY C10B3 C***TYPE DOUBLE PRECISION (BESI-S, DBESI-D) C***KEYWORDS I BESSEL FUNCTION, SPECIAL FUNCTIONS C***AUTHOR Amos, D. E., (SNLA) C Daniel, S. L., (SNLA) C***DESCRIPTION C C Abstract **** a double precision routine **** C DBESI computes an N member sequence of I Bessel functions C I/sub(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions C EXP(-X)*I/sub(ALPHA+K-1)/(X), K=1,...,N for nonnegative ALPHA C and X. A combination of the power series, the asymptotic C expansion for X to infinity, and the uniform asymptotic C expansion for NU to infinity are applied over subdivisions of C the (NU,X) plane. For values not covered by one of these C formulae, the order is incremented by an integer so that one C of these formulae apply. Backward recursion is used to reduce C orders by integer values. The asymptotic expansion for X to C infinity is used only when the entire sequence (specifically C the last member) lies within the region covered by the C expansion. Leading terms of these expansions are used to test C for over or underflow where appropriate. 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 are set to zero. An overflow C cannot occur with scaling. 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 KODE - a parameter to indicate the scaling option C KODE=1 returns C Y(K)= I/sub(ALPHA+K-1)/(X), C K=1,...,N C KODE=2 returns C Y(K)=EXP(-X)*I/sub(ALPHA+K-1)/(X), C K=1,...,N 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 I/sub(ALPHA+K-1)/(X) or scaled C values for EXP(-X)*I/sub(ALPHA+K-1)/(X), C K=1,...,N depending on KODE 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 Overflow with KODE=1 - 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, DASYIK, 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 DBESI