Given a sequence g[subscript k] greater than 0, the "g-factorial" product [big product][superscript k] [subscript i=1] g[subscript i] is extended from integer k to real x by generalizing properties of the gamma function [Gamma](x). The Euler-Mascheroni constant [gamma] and the beta and zeta functions are also generalized. Specific examples include extending the Fibonacci factorial (k!)[subscript F]= [big product][superscript k] [subscript i=1]F[subscript i] to the reals. (Contains 2 figures.)