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

Table of contents


NAME

vsbisf, vsbis, vsbisl, vsbisw, vsbisq, vsbisll, vsbisdf, vsbisd, vsbisdl, vsbisdll - vector of exponentially-scaled modified spherical Bessel functions of first kind and orders 0 to n

SYNOPSIS

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

#include <mathcw.h>

extern void vsbisf (int n, float is[/* n+1 */], float x);

extern void vsbis (int n, double is[/* n+1 */], double x);

extern void vsbisl (int n, long double is[/* n+1 */], long double x);

extern void vsbisw (int n, __float80 is[/* n+1 */], __float80 x);

extern void vsbisq (int n, __float128 is[/* n+1 */], __float128 x);

extern void vsbisll (int n, long_long_double is[/* n+1 */], long_long_double x);

extern void vsbisdf (int n, decimal_float is[/* n+1 */], decimal_float x);

extern void vsbisd (int n, decimal_double is[/* n+1 */], decimal_double x);

extern void vsbisdl (int n, decimal_long_double decimal_long_double is[/* n+1 */],
                  decimal_long_double x);

extern void vsbisdll (int n, decimal_long_long_double decimal_long_long_double is[/* n+1 */],
                   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 exponentially-scaled modified spherical Bessel function of the first kind and orders 0 through n, exp(-x) * i(0,x) through exp(-x) * i(n,x).

This function is considerably faster than one that simply invokes sbisn(k,x) for each element.

The modified spherical Bessel functions provided by these software implementations are defined according to Chapter 9, Bessel Functions of Integer 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 I(n,x) functions grow exponentially with increasing x, and overflow even with moderate x values. For that reason, this function family returns values of this Bessel function reduced by a factor of exp(-x); see vbi(3CW) for the unscaled companions.


RETURN VALUES

If the argument is finite, its exponentially-scaled first n + 1 Bessel function values of the first kind are returned in the output array, is[]. Otherwise, quiet NaNs are returned in that array.

ERRORS

If the argument x is a NaN, errno is set to EDOM, and that NaN is returned in the elements of the output array.

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), sbkn(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), vsbj(3CW), vsbk(3CW), vsbks(3CW), vsby(3CW), y0(3CW), y1(3CW), yn(3CW).