*DECK BESYNU SUBROUTINE BESYNU (X, FNU, N, Y) C***BEGIN PROLOGUE BESYNU C***SUBSIDIARY C***PURPOSE Subsidiary to BESY C***LIBRARY SLATEC C***TYPE SINGLE PRECISION (BESYNU-S, DBSYNU-D) C***AUTHOR Amos, D. E., (SNLA) C***DESCRIPTION C C Abstract C BESYNU computes N member sequences of Y Bessel functions C Y/SUB(FNU+I-1)/(X), I=1,N for non-negative orders FNU and C positive X. Equations of the references are implemented on C small orders DNU for Y/SUB(DNU)/(X) and Y/SUB(DNU+1)/(X). C Forward recursion with the three term recursion relation C generates higher orders FNU+I-1, I=1,...,N. C C To start the recursion FNU is normalized to the interval C -0.5.LE.DNU.LT.0.5. A special form of the power series is C implemented on 0.LT.X.LE.X1 while the Miller algorithm for the C K Bessel function in terms of the confluent hypergeometric C function U(FNU+0.5,2*FNU+1,I*X) is implemented on X1.LT.X.LE.X C Here I is the complex number SQRT(-1.). C For X.GT.X2, the asymptotic expansion for large X is used. C When FNU is a half odd integer, a special formula for C DNU=-0.5 and DNU+1.0=0.5 is used to start the recursion. C C BESYNU assumes that a significant digit SINH(X) function is C available. C C Description of Arguments C C Input C X - X.GT.0.0E0 C FNU - Order of initial Y function, FNU.GE.0.0E0 C N - Number of members of the sequence, N.GE.1 C C Output C Y - A vector whose first N components contain values C for the sequence Y(I)=Y/SUB(FNU+I-1), I=1,N. C C Error Conditions C Improper input arguments - a fatal error C Overflow - a fatal error C C***SEE ALSO BESY C***REFERENCES N. M. Temme, On the numerical evaluation of the ordinary C Bessel function of the second kind, Journal of C Computational Physics 21, (1976), pp. 343-350. C N. M. Temme, On the numerical evaluation of the modified C Bessel function of the third kind, Journal of C Computational Physics 19, (1975), pp. 324-337. C***ROUTINES CALLED GAMMA, R1MACH, XERMSG C***REVISION HISTORY (YYMMDD) C 800501 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) 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 900328 Added TYPE section. (WRB) C 900727 Added EXTERNAL statement. (WRB) C 910408 Updated the AUTHOR and REFERENCES sections. (WRB) C 920501 Reformatted the REFERENCES section. (WRB) C***END PROLOGUE BESYNU