function mgf( t, alpha, beta ) {
	var summand;
	var denom;
	var sum;
	var c;
	var k;

	denom = betaFcn( alpha, beta );
	sum = 1.0;
	c = 1.0;
	k = 1;
	do {
		c *= t / k;
		summand = ( betaFcn( alpha+k, beta ) / denom ) * c;
		sum += summand;
		k += 1;
	} while ( abs( summand / sum ) >= EPS );
	return sum;
}
Evaluates the moment-generating function (MGF) for a beta distribution with first shape parameter `alpha` and second shape parameter `beta` at a value `t`.

@private
@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