A Generalized Apery Series
arXiv:1204.1078
Abstract
The inverse central binomial series {equation}S_k(z)=\sum_{n=1}^{\infty}\frac{n^k z^n}{\binom{2n}{n}}{equation} popularized by Apéry and Lehmer is evaluated for positive integers along with the asymptotic behavior for large . It is found that value , as commented on by D. H. Lehmer provides a unique relation to .
7 pages