function mgf( t, alpha, beta ) {
	if (
		isnan( t ) ||
		isnan( alpha ) ||
		isnan( beta ) ||
		alpha <= 0.0 ||
		beta <= 0.0
	) {
		return NaN;
	}
	return mgf0( t, alpha, beta );
}
Evaluates the moment-generating function (MGF) for a beta distribution with first shape parameter `alpha` and second shape parameter `beta` at a value `t`.

@param {number} t - input value
@param {PositiveNumber} alpha - first shape parameter
@param {PositiveNumber} beta - second shape parameter
@returns {number} evaluated MGF

@example
var y = mgf( 0.5, 1.0, 1.0 );
// returns ~1.297

@example
var y = mgf( 0.5, 2.0, 4.0 );
// returns ~1.186

@example
var y = mgf( 3.0, 2.0, 2.0 );
// returns ~5.575

@example
var y = mgf( -0.8, 4.0, 4.0 );
// returns ~0.676

@example
var y = mgf( NaN, 1.0, 1.0 );
// returns NaN

@example
var y = mgf( 0.0, NaN, 1.0 );
// returns NaN

@example
var y = mgf( 0.0, 1.0, NaN );
// returns NaN

@example
var y = mgf( 2.0, -1.0, 0.5 );
// returns NaN

@example
var y = mgf( 2.0, 0.0, 0.5 );
// returns NaN

@example
var y = mgf( 2.0, 0.5, -1.0 );
// returns NaN

@example
var y = mgf( 2.0, 0.5, 0.0 );
// returns NaN