dbsynu.f
SUBROUTINE DBSYNU (X, FNU, N, Y)
C***BEGIN PROLOGUE DBSYNU
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Warning: this routine is not intended to be user-callable.
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C***SUBSIDIARY
C***PURPOSE Subsidiary to DBESY
C***LIBRARY SLATEC
C***TYPE DOUBLE PRECISION (BESYNU-S, DBSYNU-D)
C***AUTHOR Amos, D. E., (SNLA)
C***DESCRIPTION
C
C Abstract **** A DOUBLE PRECISION routine ****
C DBSYNU 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 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 DBSYNU assumes that a significant digit SINH function is
C available.
C
C Description of Arguments
C
C INPUT
C X - X.GT.0.0D0
C FNU - Order of initial Y function, FNU.GE.0.0D0
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 DBESY
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 D1MACH, DGAMMA, XERMSG
C***REVISION HISTORY (YYMMDD)
C 800501 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890911 Removed unnecessary intrinsics. (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 DBSYNU