digamma

Digamma function.

The digamma function ψ is the logarithmic derivative of the gamma function, i.e.

Installation

npm install @stdlib/math-base-special-digamma

Usage

var digamma = require( '@stdlib/math-base-special-digamma' );

digamma( x )

Evaluates the digamma function.

var v = digamma( -2.5 );
// returns ~1.103

v = digamma( 1.0 );
// returns ~-0.577

v = digamma( 10.0 );
// returns ~2.252

If x is 0 or a negative integer, the function returns NaN.

var v = digamma( 0.0 );
// returns NaN

v = digamma( -1.0 );
// returns NaN

v = digamma( -2.0 );
// returns NaN

If provided NaN, the function returns NaN.

var v = digamma( NaN );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var digamma = require( '@stdlib/math-base-special-digamma' );

var x;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    x = (randu()*10.0) - 5.0;
    v = digamma( x );
    console.log( 'x: %d, f(x): %d', x, v );
}

C APIs

Usage

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

stdlib_base_digamma( x )

Evaluates the digamma function.

double out = stdlib_base_digamma( -2.5 );
// returns ~1.103

out = stdlib_base_digamma( 1.0 );
// returns ~-0.577

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_digamma( const double x );

Examples

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

int main( void ) {
    const double x[] = { 4.0, -1.5, -0.5, 0.5 };

    double y;
    int i;
    for ( i = 0; i < 4; i++ ) {
        y = stdlib_base_digamma( x[ i ] );
        printf( "digamma(%lf) = %lf\n", x[ i ], y );
    }
}

See Also

• @stdlib/math-base/special/gamma: gamma function.
• @stdlib/math-base/special/trigamma: trigamma function.

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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