I0 3CW "22 April 2008" "mathcw-1.00"

Table of contents


NAME

i0f, i0, i0l, i0w, i0q, i0ll, i0df, i0d, i0dl, i0dll - modified Bessel function of first kind and order 0

SYNOPSIS

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

#include <mathcw.h>

extern float i0f (float x);

extern double i0 (double x);

extern long double i0l (long double x);

extern __float80 i0w (__float80 x);

extern __float128 i0q (__float128 x);

extern long_long_double i0ll (long_long_double x);

extern decimal_float i0df (decimal_float x);

extern decimal_double i0d (decimal_double x);

extern decimal_long_double i0dl (decimal_long_double x);

extern decimal_long_long_double i0dll (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 Bessel function of the first kind and order 0, I(0,x).

The modified 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, there is a related family of functions that return values of this Bessel function reduced by a factor of exp(-x); see i0s(3CW).


RETURN VALUES

If the argument is finite, its modified Bessel function value of the first kind and order 0 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

i0s(3CW), i1(3CW), i1s(3CW), in(3CW), ins(3CW), j0(3CW), j1(3CW), jn(3CW), k0(3CW), k0s(3CW), k1(3CW), k1s(3CW), kn(3CW), kns(3CW), vi(3CW), vis(3CW), vj(3CW), vk(3CW), vks(3CW), vy(3CW), y0(3CW), y1(3CW), yn(3CW).