A New Representation Formula for the Factorial Function

Cristinel Mortici

Abstract

We discuss in this paper a double inequality related with the factorial function due to J. Sandor and L. Debnath [On certain inequalities involving the constant e and their applications J. Math. Anal. Appl. 249 (2000) 569-582]. We establish here an asymptotic exapansion, leading to a new accurate approximation formula which provides all exact digits of n!, for every $n \leq 28$.