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 math-riemann-zeta

Usage

var zeta = require( 'math-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 );
// returns 0

v = zeta( 70 );
// returns 1

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

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

v = zeta( NaN );
// returns NaN

Examples

var linspace = require( 'compute-linspace' );
var zeta = require( 'math-riemann-zeta' );

var s = linspace( -50, 50, 200 );
var v;
var i;

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

To run the example code from the top-level application directory,

$ node ./examples/index.js

Tests

Unit

This repository uses tape for unit tests. To run the tests, execute the following command in the top-level application directory:

$ make test

All new feature development should have corresponding unit tests to validate correct functionality.

Test Coverage

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

$ make test-cov

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

$ make view-cov

Browser Support

This repository uses Testling for browser testing. To run the tests in a (headless) local web browser, execute the following command in the top-level application directory:

$ make test-browsers

To view the tests in a local web browser,

$ make view-browser-tests

License

MIT license.

Copyright

Copyright © 2016. The Compute.io Authors.