  # Manual Pages  — J0

### NAME

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

### LIBRARY

Math Library (libm, -lm)

### SYNOPSIS

`#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(), j0f(), j1(), and j1f() compute the Bessel function of the first kind of orders 0 and 1 for the real value x; the functions jn() and jnf() compute the Bessel function of the first kind of the integer order n for the real value x.

The functions y0(), y0f(), y1(), and y1f() compute the linearly independent Bessel function of the second kind of orders 0 and 1 for the positive real value x; the functions yn() and ynf() compute the Bessel function of the second kind for the integer order n for the positive real value x.

### RETURN VALUES

These routines return values of their respective Bessel functions. For large positive inputs, they may underflow and return &#177;0.

The following applies to y0(), y0f(), y1(), y1f(), yn(), and ynf(). If x is negative, including -∞, these routines will generate an invalid exception and return NaN. If x is &#177;0, these routines will generate a divide-by-zero exception and return -∞. If x is a sufficiently small positive number, then y1(), y1f(), yn(), and ynf() will generate an overflow exception and return -∞.

### STANDARDS

The j0(), j1(), jn(), y0(), y1(), and yn() functions conform to IEEE Std 1003.1-2001 ("POSIX.1"). The float versions are extensions.

### HISTORY

This set of functions appeared in AT&T v7 .

 J0 (3) March 10, 2015  