BESYNU(3)

SYNOPSIS
SUBROUTINE BESYNU (X, FNU, N, Y)

NAME
besynu - Subsidiary to BESY

LIBRARY
SLATEC

TYPE
SINGLE PRECISION (BESYNU-S, DBSYNU-D)

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract BESYNU computes N member sequences of Y Bessel functions Y/SUB(FNU+I-1)/(X), I=1,N for non-negative orders FNU and positive X. Equations of the references are implemented on small orders DNU for Y/SUB(DNU)/(X) and Y/SUB(DNU+1)/(X). Forward recursion with the three term recursion relation generates higher orders FNU+I-1, I=1,...,N. To start the recursion FNU is normalized to the interval -0.5.LE.DNU.LT.0.5. A special form of the power series is implemented on 0.LT.X.LE.X1 while the Miller algorithm for the K Bessel function in terms of the confluent hypergeometric function U(FNU+0.5,2*FNU+1,I*X) is implemented on X1.LT.X.LE.X Here I is the complex number SQRT(-1.). For X.GT.X2, the asymptotic expansion for large X is used. When FNU is a half odd integer, a special formula for DNU=-0.5 and DNU+1.0=0.5 is used to start the recursion. BESYNU assumes that a significant digit SINH(X) function is available. Description of Arguments Input X - X.GT.0.0E0 FNU - Order of initial Y function, FNU.GE.0.0E0 N - Number of members of the sequence, N.GE.1 Output Y - A vector whose first N components contain values for the sequence Y(I)=Y/SUB(FNU+I-1), I=1,N. Error Conditions Improper input arguments - a fatal error Overflow - a fatal error

SEE ALSO
BESY

REFERENCES
N. M. Temme, On the numerical evaluation of the ordinary Bessel function of the second kind, Journal of Computational Physics 21, (1976), pp. 343-350. N. M. Temme, On the numerical evaluation of the modified Bessel function of the third kind, Journal of Computational Physics 19, (1975), pp. 324-337.

ROUTINES CALLED
GAMMA, R1MACH, XERMSG

REVISION HISTORY (YYMMDD)
800501 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
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)
900328 Added TYPE section. (WRB)
900727 Added EXTERNAL statement. (WRB)
910408 Updated the AUTHOR and REFERENCES sections. (WRB)
920501 Reformatted the REFERENCES section. (WRB)