# @stdlib/math-base-special-digamma

0.3.0 • Public • Published

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# 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 );
}
}```

## 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.

## Package Sidebar

### Install

`npm i @stdlib/math-base-special-digamma`

### Repository

github.com/stdlib-js/math-base-special-digamma

stdlib.io

1,459

### Version

0.3.0

Apache-2.0 AND BSL-1.0

75.4 kB

21