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

Table of contents


NAME

knf, kn, knl, knw, knq, knll, kndf, knd, kndl, kndll - modified Bessel function of second kind and order n

SKNOPSIS

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

#include <mathcw.h>

extern float knf (int n, float x);

extern double kn (int n, double x);

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

extern __float80 knw (int n, __float80 x);

extern __float128 knq (int n, __float128 x);

extern long_long_double knll (int n, long_long_double x);

extern decimal_float kndf (int n, decimal_float x);

extern decimal_double knd (int n, decimal_double x);

extern decimal_long_double kndl (int n, decimal_long_double x);

extern decimal_long_long_double kndll (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 Bessel function of the second kind and order n, K(n,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 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 kns(3CW).


RETURN VALUES

If the argument is nonnegative and finite, its modified Bessel function value of the second kind of 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.

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

If the argument is zero, errno is set to ERANGE, and a positive Infinity (or the largest floating-point magnitude, if Infinity is not available) is returned.


SEE ALSO

i0(3CW), i0s(3CW), i1(3CW), i1s(3CW), in(3CW), ins(3CW), j0(3CW), j1(3CW), jn(3CW), k0(3CW), k0s(3CW), k1(3CW), k1s(3CW), kns(3CW), vi(3CW), vis(3CW), vj(3CW), vk(3CW), vks(3CW), vy(3CW), y0(3CW), y1(3CW), yn(3CW).