@stdlib/math-base-special-riemann-zeta
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0.0.6 • Public • Published

Riemann Zeta Function

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Riemann zeta function.

The Riemann zeta function is the analytic continuation of the infinite series

Riemann zeta function

where s is a complex variable equal to σ + ti. The series is only convergent when the real part of s, σ, is greater than 1.

Installation

npm install @stdlib/math-base-special-riemann-zeta

Usage

var zeta = require( '@stdlib/math-base-special-riemann-zeta' );

zeta( s )

Evaluates the Riemann zeta function as a function of a real variable s (i.e., t = 0).

var v = zeta( 1.1 );
// returns ~10.584

v = zeta( -4.0 );
// returns 0.0

v = zeta( 70.0 );
// returns 1.0

v = zeta( 0.5 );
// returns ~-1.46

v = zeta( 1.0 ); // pole
// returns NaN

v = zeta( NaN );
// returns NaN

Examples

var linspace = require( '@stdlib/array-base-linspace' );
var zeta = require( '@stdlib/math-base-special-riemann-zeta' );

var s = linspace( -50.0, 50.0, 200 );

var i;
for ( i = 0; i < s.length; i++ ) {
    console.log( 's: %d, ζ(s): %d', s[ i ], zeta( s[ i ] ) );
}

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.

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License

See LICENSE.

Copyright

Copyright © 2016-2022. The Stdlib Authors.

Install

npm i @stdlib/math-base-special-riemann-zeta

Homepage

stdlib.io

DownloadsWeekly Downloads

165

Version

0.0.6

License

Apache-2.0 AND BSL-1.0

Unpacked Size

81 kB

Total Files

21

Last publish

Collaborators

  • stdlib-bot
  • kgryte
  • planeshifter
  • rreusser