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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var zeta = require( '@stdlib/math-base-special-riemann-zeta' );

var opts = {
    'dtype': 'float64'
};
var s = uniform( 200, -50.0, 50.0, opts );

logEachMap( 's: %0.4f, ζ(s): %0.4f', s, zeta );

C APIs

Usage

#include "stdlib/math/base/special/riemann_zeta.h"

stdlib_base_zeta( s )

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

double out = stdlib_base_zeta( 1.1 );
// returns ~10.584

The function accepts the following arguments:

• s: [in] double input value.

double stdlib_base_zeta( const double s );

Examples

#include "stdlib/math/base/special/riemann_zeta.h"
#include <stdio.h>

int main( void ) {
    const double s[] = { -50.0, -38.9, -27.8, -16.7, -5.6, 5.6, 16.7, 27.8, 38.9, 50.0 };

    double v;
    int i;
    for ( i = 0; i < 10; i++ ) {
        v = stdlib_base_zeta( s[ i ] );
        printf( "zeta(%lf) = %lf\n", s[ i ], v );
    }
}

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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Copyright

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