---
name: "j0"
section: "3"
platform: "linux"
package: "man-pages"
version: "6.19-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/j0"
---

# j0(3)

Bessel functions of the first kind

## NAME

j0, j0f, j0l, j1, j1f, j1l, jn, jnf, jnl - Bessel functions of the first kind

## LIBRARY

Math library (*libm*, *-lm*)

## SYNOPSIS

```
#include <math.h>
```

**double j0(double** *x***);** **double j1(double** *x***);** **double jn(int** *n***, double** *x***);**

**float j0f(float** *x***);** **float j1f(float** *x***);** **float jnf(int** *n***, float** *x***);**

**long double j0l(long double** *x***);** **long double j1l(long double** *x***);** **long double jnl(int** *n***, long double** *x***);**

Feature Test Macro Requirements for glibc (see [**feature\_test\_macros**(7)](/feature_test_macros/7.md)):

**j0**(), **j1**(), **jn**():

```
    _XOPEN_SOURCE
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
```

**j0f**(), **j0l**(), **j1f**(), **j1l**(), **jnf**(), **jnl**():

```
    _XOPEN_SOURCE >= 600
        || (_ISOC99_SOURCE && _XOPEN_SOURCE)
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
```

## DESCRIPTION

The **j0**() and **j1**() functions return Bessel functions of *x* of the first kind of orders 0 and 1, respectively. The **jn**() function returns the Bessel function of *x* of the first kind of order *n*.

The **j0f**(), **j1f**(), and **jnf**(), functions are versions that take and return *float* values. The **j0l**(), **j1l**(), and **jnl**() functions are versions that take and return *long double* values.

## RETURN VALUE

On success, these functions return the appropriate Bessel value of the first kind for *x*.

If *x* is a NaN, a NaN is returned.

If *x* is too large in magnitude, or the result underflows, a range error occurs, and the return value is 0.

## ERRORS

See [**math\_error**(7)](/math_error/7.md) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:

- Range error: result underflow, or *x* is too large in magnitude

  *errno* is set to **ERANGE**.

These functions do not raise exceptions for [**fetestexcept**(3)](/fetestexcept/3.md).

## ATTRIBUTES

For an explanation of the terms used in this section, see [**attributes**(7)](/attributes/7.md).

| | | |
| --- | --- | --- |
| **Interface** | **Attribute** | **Value** |
| **j0**(), **j0f**(), **j0l**() | Thread safety | MT-Safe |
| **j1**(), **j1f**(), **j1l**() | Thread safety | MT-Safe |
| **jn**(), **jnf**(), **jnl**() | Thread safety | MT-Safe |

## STANDARDS

- **j0**() **j1**() **jn**()

  POSIX.1-2008.

- Others:

  BSD.

## HISTORY

- **j0**() **j1**() **jn**()

  SVr4, 4.3BSD, POSIX.1-2001, POSIX.1-2008.

- Others:

  BSD.

## BUGS

There are errors of up to 2e-16 in the values returned by **j0**(), **j1**(), and **jn**() for values of *x* between -8 and 8.

## SEE ALSO

[**y0**(3)](/y0/3.md)