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# npm

## @stdlib/math-base-special-bernoulli

0.0.6 • Public • Published

# Bernoulli

Compute the nth Bernoulli number.

## Installation

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

## Usage

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

#### bernoulli( n )

Computes the nth Bernoulli number.

```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 cannot be safely represented in double-precision floating-point format.

```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`.

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

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

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

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

## Examples

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

var v;
var i;

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

## Notice

This package is part of 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, see the main project repository.

## Keywords

### Install

`npm i @stdlib/math-base-special-bernoulli`

stdlib.io

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