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Bernoulli

Compute the nth Bernoulli number.

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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 );
}

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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 );
// returns 1.0

out = stdlib_base_bernoulli( 1 );
// returns 0.5

The function accepts the following arguments:

• n: [in] int32_t input value.

double stdlib_base_bernoulli( const int32_t n );

Examples

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

int main( void ) {
    int32_t i;
    double v;

    for ( i = 0; i < 130; i++ ) {
        v = stdlib_base_bernoulli( i );
        printf( "bernoulli(%d) = %lf\n", i, v );
    }
}

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.