Trigamma

Trigamma function.

The trigamma function ψ^(1) is the derivative of the digamma function.

psi Superscript left-parenthesis 1 right-parenthesis Baseline left-parenthesis x right-parenthesis equals StartFraction d Over d x EndFraction normal upper Psi left-parenthesis x right-parenthesis equals sigma-summation Underscript k equals 0 Overscript normal infinity Endscripts StartFraction 1 Over left-parenthesis k plus x right-parenthesis squared EndFraction

Usage

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

trigamma( x )

Evaluates the trigamma function.

var v = trigamma( -2.5 );
// returns ~9.539

v = trigamma( 1.0 );
// returns ~1.645

v = trigamma( 10.0 );
// returns ~0.105

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

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

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

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

If provided NaN, the function returns NaN.

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

Examples

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

var x;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    x = (randu()*100.0) - 50.0;
    v = trigamma( x );
    console.log( 'x: %d, ψ^(1)(x): %d', x, v );
}