/**
 * gamma function
 * @param z Only works for 1 <= z <= 142 but also defined for non integers.
 * @returns approximation to (z-1)!
 * @author Roedy Green email
 */
static double gamma (double z)
   {
   return Math.exp( -z ) * Math.pow( z, z-0.5 )* Math.sqrt( 2 * Math.PI ) *
   (1 + 1/( 12* z ) + 1 / ( 288* z * z)-139 / (51840 * z * z*z ) - 571 / ( 2488320 * z * z * z *z ));
   }