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<!--
@license Apache-2.0
Copyright (c) 2018 The Stdlib Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
-->
# Bernoulli
> Compute the nth [Bernoulli number][bernoulli-number].
<section class="intro">
<!-- /.intro -->
<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 0.0
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 -->
<section class="links">
[bernoulli-number]: https://en.wikipedia.org/wiki/Bernoulli_number
[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
</section>
<!-- /.links -->
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