cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ] #include <mathcw.h> extern void vsbif (int n, float i[/* n+1 */], float x); extern void vsbi (int n, double i[/* n+1 */], double x); extern void vsbil (int n, long double i[/* n+1 */], long double x); extern void vsbiw (int n, __float80 i[/* n+1 */], __float80 x); extern void vsbiq (int n, __float128 i[/* n+1 */], __float128 x); extern void vsbill (int n, long_long_double i[/* n+1 */], long_long_double x); extern void vsbidf (int n, decimal_float i[/* n+1 */], decimal_float x); extern void vsbid (int n, decimal_double i[/* n+1 */], decimal_double x); extern void vsbidl (int n, decimal_long_double decimal_long_double i[/* n+1 */], decimal_long_double x); extern void vsbidll (int n, decimal_long_long_double decimal_long_long_double i[/* 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 sbin(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).
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 vsbis(3CW).