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 0.5

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 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 );
}

C APIs

Usage

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

stdlib_base_bernoulli( n )

Computes the nth Bernoulli number.

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.

double stdlib_base_bernoulli( const double n );

Examples

#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 );
    }
}

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.