AN APPROXIMATION FORMULA FOR THE WALLIS RATIO IN A SIMPLE FORM

We present a different point of view for improving some approximation formulas for the Wallis ratio. In many published papers several such improvements were announced by adding terms from an asymptotic expansion to an already stated approximation formula. This addition can be done to almost every approximation formula involving the gamma function, or ratio of gamma functions. Unfortunately, these new approximation formulas are obtained via a sacrifice of simplicity. One of the approximation formula for the Wallis ratio of a simple form stated here is the following: (2n-1)‼/(2n)‼~1/√eπn (1+1/2n)^(n-1/(12n+3)) , n→∞. Then other formulas are given and a general method for obtaining similar formulas is presented.