npm package: @stdlib/math-base-special-bernoulli
Description: Compute the nth Bernoulli number.
Author: The Stdlib Authors
Latest version: 0.4.1

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# Bernoulli

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the nth [Bernoulli number][bernoulli-number].

<section class="intro">

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-bernoulli
```

</section>

<section class="usage">

## Usage

```javascript
var bernoulli = require( '@stdlib/math-base-special-bernoulli' );
```

#### bernoulli( n )

Computes the nth [Bernoulli number][bernoulli-number].

```javascript
var v = bernoulli( 0 );
// returns 1.0

v = bernoulli( 1 );
// returns 0.5

v = bernoulli( 2 );
// returns ~0.167

v = bernoulli( 3 );
// returns 0.0

v = bernoulli( 4 );
// returns ~-0.033

v = bernoulli( 5 );
// returns 0.0

v = bernoulli( 20 );
// returns ~-529.124
```

For even integers `n >= 260`, the function alternates between returning positive and negative infinity, as larger [Bernoulli numbers][bernoulli-number] cannot be safely represented in [double-precision floating-point format][ieee754].

```javascript
var v = bernoulli( 260 );
// returns -Infinity

v = bernoulli( 262 );
// returns Infinity

v = bernoulli( 264 );
// returns -Infinity
```

If not provided a nonnegative integer value, the function returns `NaN`.

```javascript
var v = bernoulli( 3.14 );
// returns NaN

v = bernoulli( -1 );
// returns NaN
```

If provided `NaN`, the function returns `NaN`.

```javascript
var v = bernoulli( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var bernoulli = require( '@stdlib/math-base-special-bernoulli' );

var v;
var i;

for ( i = 0; i < 280; i++ ) {
    v = bernoulli( i );
    console.log( v );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/bernoulli.h"
```

#### stdlib_base_bernoulli( n )

Computes the nth [Bernoulli number][bernoulli-number].

```c
double out = stdlib_base_bernoulli( 0.0 );
// returns 1.0

out = stdlib_base_bernoulli( 1.0 );
// returns 0.5
```

The function accepts the following arguments:

-   **n**: `[in] double` input value.

```c
double stdlib_base_bernoulli( const double n );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/bernoulli.h"
#include <stdio.h>

int main( void ) {
    double i;
    double v;

    for ( i = 0.0; i < 130.0; i++ ) {
        v = stdlib_base_bernoulli( i );
        printf( "bernoulli(%lf) = %lf\n", i, v );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-bernoulli/main/LICENSE

[bernoulli-number]: https://en.wikipedia.org/wiki/Bernoulli_number

[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

</section>

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