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    math-dirichlet-eta

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    Dirichlet Eta Function

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    Dirichlet eta function.

    The Dirichlet eta function is defined by the Dirichlet series

    Dirichlet eta function

    where s is a complex variable equal to σ + ti. The series is convergent for all complex numbers having a real part greater than 0.

    Note that the Dirichlet eta function is also known as the alternating zeta function and denoted ζ*(s). The series is an alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function. Accordingly, the following relation holds:

    Dirichlet-Riemann zeta relation

    where ζ(s) is the Riemann zeta function.

    Installation

    $ npm install math-dirichlet-eta

    Usage

    var eta = require( 'math-dirichlet-eta' );

    eta( s )

    Evaluates the Dirichlet eta function as a function of a real variable s.

    var v = eta( 0 ); // Abel sum of 1-1+1-1+...
    // returns 0.5
     
    = eta( -1.0 ); // Abel sum of 1-2+3-4+...
    // returns 0.25
     
    = eta( 1.0 ); // alternating harmonic series
    // returns 0.6931471805599453 => ln(2)
     
    = eta( 3.14 );
    // returns ~0.9096
     
    = eta( NaN );
    // returns NaN

    Examples

    var linspace = require( 'compute-linspace' );
    var eta = require( 'math-dirichlet-eta' );
     
    var s = linspace( -50, 50, 200 );
    var v;
    var i;
     
    for ( i = 0; i < s.length; i++ ) {
        v = eta( s[ i ] );
        console.log( 's: %d, η(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.

    Install

    npm i math-dirichlet-eta

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    Version

    1.0.0

    License

    MIT

    Last publish

    Collaborators

    • kgryte