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

Table of contents


NAME

vbyf, vby, vbyl, vbyw, vbyq, vbyll, vbydf, vbyd, vbydl, vbydll - vector of ordinary Bessel functions of second kind and orders 0 to n

SYNOPSIS

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

#include <mathcw.h>

extern void vbyf (int n, float Y[/* n+1 */], float x);

extern void vby (int n, double Y[/* n+1 */], double x);

extern void vbyl (int n, long double Y[/* n+1 */], long double x);

extern void vbyw (int n, __float80 Y[/* n+1 */], __float80 x);

extern void vbyq (int n, __float128 Y[/* n+1 */], __float128 x);

extern void vbyll (int n, long_long_double Y[/* n+1 */], long_long_double x);

extern void vbydf (int n, decimal_float Y[/* n+1 */], decimal_float x);

extern void vbyd (int n, decimal_double Y[/* n+1 */], decimal_double x);

extern void vbydl (int n, decimal_long_double decimal_long_double Y[/* n+1 */],
                  decimal_long_double x);

extern void vbydll (int n, decimal_long_long_double decimal_long_long_double Y[/* n+1 */],
                   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 ordinary Bessel function of the second kind and orders 0 through n, Y(0,x) through Y(n,x).

This function is considerably faster than one that simply invokes yn(k,x) for each element.

The ordinary 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 recurrence relations used to generate sequences of Bessel function values necessarily lose accuracy near the uncountably-many zeros of the function, so only low absolute, rather than relative, accuracy can be expected. For high relative accuracy in the working precision, use the function for the next higher precision, if that is available.


RETURN VALUES

If the argument is finite, its first n + 1 Bessel function values of the second kind are returned in the output array, Y[]. Otherwise, quiet NaNs are returned in that array.

ERRORS

If the argument x is a NaN, errno is set to EDOM, and that NaN is returned in the elements of the output array.

If the argument x is negative, errno is set to EDOM, and a quiet NaN is returned in the elements of the output array.

If the argument x is zero, errno is set to ERANGE, and a negative Infinity (or the negative of the largest floating-point magnitude, if Infinity is not available) is returned in the elements of the output array.


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), sbi1(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), vsbi(3CW), vsbis(3CW), vsbj(3CW), vsbk(3CW), vsbks(3CW), vsby(3CW), y0(3CW), y1(3CW), yn(3CW).