Normalized Hermite Polynomial

Evaluate a normalized Hermite polynomial.

The normalized (aka "probabilist") Hermite polynomials are given by

Usage

var normhermitepoly = require( '@stdlib/math/base/tools/normhermitepoly' );

normhermitepoly( n, x )

Evaluates a normalized Hermite polynomial of degree n.

var v = normhermitepoly( 1, 1.0 );
// returns 1.0

v = normhermitepoly( 1, 0.5 );
// returns 0.5

v = normhermitepoly( 0, 0.5 );
// returns 1.0

v = normhermitepoly( 2, 0.5 );
// returns -0.75

v = normhermitepoly( -1, 0.5 );
// returns NaN

normhermitepoly.factory( n )

Returns a function for evaluating a normalized Hermite polynomial of degree n.

var polyval = normhermitepoly.factory( 2 );

var v = polyval( 0.5 );
// returns -0.75

Examples

var randu = require( '@stdlib/random/base/randu');
var normhermitepoly = require( '@stdlib/math/base/tools/normhermitepoly' );

var xx;
var yy;
var x;
var y;
var i;
var j;

for ( i = 0; i < 100; i++ ) {
    x = (randu()*100.0) - 50.0;
    for ( j = 1; j < 3; j++ ) {
        y = normhermitepoly( j, x );
        xx = x.toFixed(3);
        yy = y.toFixed(3);
        console.log( 'He_%d( %d ) = %d', j, xx, yy );
    }
}