The Asymptotics of Factorials, Binomial Coefficients and Catalan Numbers

We present a variety of not-well-known asymptotic series for factorials, binomial coefficients and Catalan numbers, all having only even or odd powers. We discuss the significance of this property in terms of the asymptotic evenness or oddness of the underlying quantities.

Automated summary

This article presents a variety of not-well-known asymptotic series for factorials, binomial coefficients, and Catalan numbers, all of which only have even or odd powers. The significance of this property is discussed in terms of the asymptotic evenness or oddness of the underlying quantities.