SBI1 3CW "22 April 2008" "mathcw-1.00"

Table of contents


NAME

sbi1f, sbi1, sbi1l, sbi1w, sbi1q, sbi1ll, sbi1df, sbi1d, sbi1dl, sbi1dll - modified spherical Bessel function of first kind and order 1

SYNOPSIS

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

#include <mathcw.h>

extern float sbi1f (float x);

extern double sbi1 (double x);

extern long double sbi1l (long double x);

extern __float80 sbi1w (__float80 x);

extern __float128 sbi1q (__float128 x);

extern long_long_double sbi1ll (long_long_double x);

extern decimal_float sbi1df (decimal_float x);

extern decimal_double sbi1d (decimal_double x);

extern decimal_long_double sbi1dl (decimal_long_double x);

extern decimal_long_long_double sbi1dll (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 first kind and order 1, i(1,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 i(n,x) functions grow exponentially with increasing x, and overflow even with moderate x values. For that reason, there is a related family of functions that return values of this Bessel function reduced by a factor of exp(-x); see bis1(3CW).


RETURN VALUES

If the argument is finite, its modified spherical Bessel function value of the first kind and order 1 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), 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), vsbis(3CW), vsbj(3CW), vsbk(3CW), vsbks(3CW), vsby(3CW), y0(3CW), y1(3CW), yn(3CW).