J0(3) | Library Functions Manual | J0(3)

# NAME

`j0`, `j0f`, `j1`, `j1f`, `jn`, `jnf`, `y0`, `y0f`, `y1`, `y1f`, `yn`, `ynf` — Bessel functions of first and second kind

# SYNOPSIS

Math Library (libm, -lm)
`#include <math.h>`

double
`j0`(double x);

float
`j0f`(float x);

double
`j1`(double x);

float
`j1f`(float x);

double
`jn`(int n, double x);

float
`jnf`(int n, float x);

double
`y0`(double x);

float
`y0f`(float x);

double
`y1`(double x);

float
`y1f`(float x);

double
`yn`(int n, double x);

float
`ynf`(int n, float x);

# DESCRIPTION

The functions `j0`() and `j1`() compute the Bessel function of the first kind of the order 0 and the order 1, respectively, for the real value x; the function `jn`() computes the Bessel function of the first kind of the integer order n for the real value x. The functions `j0f`(), `j1f`(), and `jnf`() are single precision versions of `j0`(), `j1`(), and `jn`(), respectively.

The functions `y0`() and `y1`() compute the linearly independent Bessel function of the second kind of the order 0 and the order 1, respectively, for the positive integer value x (expressed as a double); the function `yn`() computes the Bessel function of the second kind for the integer order n for the positive integer value x (expressed as a double). The functions `y0f`(), `y1f`(), and `ynf`() are single precision versions of `y0`(), `y1`(), and `yn`(), respectively.

# RETURN VALUES

If these functions are successful, the computed value is returned, otherwise the global variable errno is set to `EDOM` or `ERANGE`.

# HISTORY

The functions `j0`(), `j1`(), `jn`(), `y0`(), `y1`(), and `yn`() first appeared in Version 7 AT&T UNIX.

June 7, 2025 | Debian