BESKNU(3)

SYNOPSIS
SUBROUTINE BESKNU (X, FNU, KODE, N, Y, NZ)

NAME
besknu - Subsidiary to BESK

LIBRARY
SLATEC

TYPE
SINGLE PRECISION (BESKNU-S, DBSKNU-D)

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Abstract BESKNU computes N member sequences of K Bessel functions K/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 K/SUB(DNU)/(X) and K/SUB(DNU+1)/(X). Forward recursion with the three term recursion relation generates higher orders FNU+I-1, I=1,...,N. The parameter KODE permits K/SUB(FNU+I-1)/(X) values or scaled values EXP(X)*K/SUB(FNU+I-1)/(X), I=1,N to be returned. 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,X) is implemented on X1.LT.X.LE.X2. 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. BESKNU assumes that a significant digit SINH(X) function is available. Description of Arguments Input X - X.GT.0.0E0 FNU - Order of initial K function, FNU.GE.0.0E0 N - Number of members of the sequence, N.GE.1 KODE - A parameter to indicate the scaling option KODE= 1 returns Y(I)= K/SUB(FNU+I-1)/(X) I=1,...,N = 2 returns Y(I)=EXP(X)*K/SUB(FNU+I-1)/(X) I=1,...,N Output Y - A vector whose first N components contain values for the sequence Y(I)= K/SUB(FNU+I-1)/(X), I=1,...,N or Y(I)=EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N depending on KODE NZ - Number of components set to zero due to underflow, NZ= 0 , Normal return NZ.NE.0 , First NZ components of Y set to zero due to underflow, Y(I)=0.0E0,I=1,...,NZ Error Conditions Improper input arguments - a fatal error Overflow - a fatal error Underflow with KODE=1 - a non-fatal error (NZ.NE.0)

SEE ALSO
BESK

REFERENCES
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, I1MACH, R1MACH, XERMSG

REVISION HISTORY (YYMMDD)
790201 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)