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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.


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


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


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 ] ) );


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



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  • stdlib-bot
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