SBKN 3CW "22 April 2008" "mathcw-1.00"

Table of contents


NAME

sbknf, sbkn, sbknl, sbknw, sbknq, sbknll, sbkndf, sbknd, sbkndl, sbkndll - modified spherical Bessel function of second kind and order n

SYNOPSIS

cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ]

#include <mathcw.h>

extern float sbknf (int n, float x);

extern double sbkn (int n, double x);

extern long double sbknl (int n, long double x);

extern __float80 sbknw (int n, __float80 x);

extern __float128 sbknq (int n, __float128 x);

extern long_long_double sbknll (int n, long_long_double x);

extern decimal_float sbkndf (int n, decimal_float x);

extern decimal_double sbknd (int n, decimal_double x);

extern decimal_long_double sbkndl (int n, decimal_long_double x);

extern decimal_long_long_double sbkndll (int n, decimal_long_long_double x);

NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.


DESCRIPTION

Compute the modified spherical Bessel function of the second kind and order n, k(n,x).

The modified spherical Bessel functions provided by these software implementations are defined according to Chapter 10, Bessel Functions of Fractional Order, of the Handbook of Mathematical Functions, edited by Milton Abramowitz and Irene A. Stegun, National Bureau of Standards Applied Mathematics Series #55, US Department of Commerce, Washington, DC (1964).


CAVEAT

Although in mathematics, uppercase letters name the ordinary and modified Bessel functions, and lowercase letters name the spherical Bessel functions, the lowercase names of the POSIX Bessel functions mean the former, not the latter.

The k(n,x) functions fall exponentially with increasing x, and underflow even with moderate x values. For that reason, there is a related family of functions that return values of this Bessel function increased by a factor of exp(x); see sbksn(3CW).


RETURN VALUES

If the argument is finite, its modified spherical Bessel function value of the first kind and order n is returned. Otherwise, a quiet NaN is returned.

ERRORS

If the argument is a NaN, errno is set to EDOM, and that NaN is returned.

SEE ALSO

bi0(3CW), bi1(3CW), bin(3CW), bis0(3CW), bis1(3CW), bisn(3CW), bk0(3CW), bk1(3CW), bkn(3CW), bks0(3CW), bks1(3CW), bksn(3CW), j0(3CW), j1(3CW), jn(3CW), sbi0(3CW), sbi1(3CW), sbin(3CW), sbis0(3CW), sbis1(3CW), sbisn(3CW), sbj0(3CW), sbj1(3CW), sbjn(3CW), sbk0(3CW), sbk1(3CW), sbks0(3CW), sbks1(3CW), sbksn(3CW), sby0(3CW), sby1(3CW), sbyn(3CW), vbi(3CW), vbis(3CW), vbj(3CW), vbk(3CW), vbks(3CW), vby(3CW), vsbi(3CW), vsbis(3CW), vsbj(3CW), vsbk(3CW), vsbks(3CW), vsby(3CW), y0(3CW), y1(3CW), yn(3CW).