digamma

Digamma function.

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

psi left-parenthesis x right-parenthesis equals StartFraction d Over d x EndFraction ln normal upper Gamma left-parenthesis x right-parenthesis equals StartFraction normal upper Gamma prime left-parenthesis x right-parenthesis Over normal upper Gamma left-parenthesis x right-parenthesis EndFraction

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 );
}