cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ] #include <mathcw.h> extern void vbkf (int n, float K[/* n+1 */], float x); extern void vbk (int n, double K[/* n+1 */], double x); extern void vbkl (int n, long double K[/* n+1 */], long double x); extern void vbkw (int n, __float80 K[/* n+1 */], __float80 x); extern void vbkq (int n, __float128 K[/* n+1 */], __float128 x); extern void vbkll (int n, long_long_double K[/* n+1 */], long_long_double x); extern void vbkdf (int n, decimal_float K[/* n+1 */], decimal_float x); extern void vbkd (int n, decimal_double K[/* n+1 */], decimal_double x); extern void vbkdl (int n, decimal_long_double decimal_long_double K[/* n+1 */], decimal_long_double x); extern void vbkdll (int n, decimal_long_long_double decimal_long_long_double K[/* n+1 */], decimal_long_long_double x);
NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.
This function is considerably faster than one that simply invokes bkn(k,x) for each element.
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).
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 vbks(3CW).
If the argument is negative, errno is set to EDOM, and a quiet NaN is returned in the output array.
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 in the output array.