factorial functionSSSSS

Abstract. The Gamma function of Euler often is thought as the only function which interpolates the factorial numbers n! = 1,2,6,24,.... This is far from being true. We will discuss four factorial functions
the Euler factorial function n!,
the Hadamard Gamma function H(n),
the logarithmic single inflected factorial function L(n),
the logarithmic single inflected hyper-factorial function L*(n).

We will show that these alternative factorial functions posses qualities which are missing from the the conventional factorial function but might be desirable in some context.