Polygamma

Polygamma function.

Usage

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

polygamma( n, x )

Evaluates the polygamma function of order n; i.e., the (n+1)th derivative of the natural logarithm of the gamma function.

var v = polygamma( 3, 1.2 );
// returns ~3.245

v = polygamma( 5, 1.2 );
// returns ~41.39

v = polygamma( 3, -4.9 );
// returns ~60014.239

If n is not a nonnegative integer, the function returns NaN.

var v = polygamma( 2.5, -1.2 );
// returns NaN

v = polygamma( -1, 5.3 );
// returns NaN

If x is 0 or a negative odd integer, the function returns +Infinity.

var v = polygamma( 2, 0.0 );
// returns +Infinity

v = polygamma( 2, -1.0 );
// returns +Infinity

If x on the other hand is a negative even integer, the function returns NaN.

v = polygamma( 2, -4.0 );
// returns NaN

v = polygamma( 2, -2.0 );
// returns NaN

If provided NaN as either parameter, the function returns NaN.

var v = polygamma( NaN, 2.1 );
// returns NaN

v = polygamma( 1, NaN );
// returns NaN

v = polygamma( NaN, NaN );
// returns NaN

Examples

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

var n;
var x;
var v;
var i;

for ( i = 0; i < 100; i++ ) {
    x = (randu()*100.0) - 50.0;
    n = round( randu()*50.0 );
    v = polygamma( x, n );
    console.log( 'x: %d, ψ^(%d)(x): %d', x, n, v );
}