bessel(3) — Subroutines

NAME

bessel, j0, j1, jn, y0, y1, yn − Compute Bessel functions

SYNOPSIS

#include <math.h>
double j0(
        double x ); float j0f(
        float x ); long double j0l(
        long double x ); double j1(
        double x ); float j1f(
        float x ); long double j1l(
        long double x ); double jn(
        int n,
        double x ); float jnf(
        int n,
        float x ); long double jnl(
        int n,
        long double x ); double y0(
        double x ); float y0f(
        float x ); long double y0l(
        long double x ); double y1(
        double x ); float y1f(
        float x ); long double y1l(
        long double x ); double yn(
        int n,
        double x ); float ynf(
        int n,
        float x ); long double ynl(
        int n,
        long double x );

LIBRARY

Math Library (libm)

STANDARDS

Interfaces documented on this reference page conform to industry standards as follows:

j0(): XPG4

j1(): XPG4

jn(): XPG4

y0(): XPG4

y1(): XPG4

yn(): XPG4

Refer to the standards(5) reference page for more information about industry standards and associated tags.

DESCRIPTION

The j0(), j0f(), j0l(), j1(), j1f(), and j1l() functions return the value of the Bessel function of the first kind of orders 0 (zero) and 1, respectively.

The jn(), jnf(), and jnl() functions return the value of the Bessel function of the first kind of order n.

The y0(), y0f(), y0l(), y1(), y1f(), and y1l() functions return the value of the Bessel functions of the second kind of orders 0 (zero) and 1, respectively.

The yn(), ynf(), and ynl() functions return the value of the Bessel function of the second kind of order n.

The following table describes function behavior in response to exceptional arguments:

Function	Exceptional Argument	Routine Behavior
j0(), j1(), jn()	None	N/A
j0f(), j1f(), jnf()	None	N/A
j0l(),j1l(), jnl()	None	N/A
y0(), y1(), yn()	x < 0	Invalid argument
y0f(), y1f(), ynf()	x < 0	Invalid argument
y0l(), y1l(), ynl()	x < 0	Invalid argument
y0(), y1(), yn()	x = 0	Overflow
y0f(), y1f(), ynf()	x = 0	Overflow
y0l(), y1l(), ynl()	x = 0	Overflow

The j1() and jn() functions can result in an underflow as x gets small. The largest value of x for which this occurs is a function of n.