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

About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Riemann Zeta Function

Riemann zeta function.

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

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.

Community

---

Copyright

Copyright © 2016-2024. The Stdlib Authors.