---
name: "j0"
section: "3"
platform: "freebsd"
package: "base"
version: "16.0-CURRENT-20261027-61c70dc16a79"
release: "FreeBSD 16.0-CURRENT (2026-10-27)"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/j0"
---

# j0(3)

Bessel functions of first and second kind

## 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 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 . If *x* is 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 -.

## SEE ALSO

[math(3)](/math/3.md)

## 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 Version 7 AT&T UNIX.