A Generalized Apery Series

Details A Generalized Apery Series A Generalized Apery Series

2012-04-04

arxiv.org/abs/1204.1078v1

Mathematics

Classical Analysis and ODEs

7 pages

Scientific paper

The inverse central binomial series
{equation}S_k(z)=\sum_{n=1}^{\infty}\frac{n^k z^n}{\binom{2n}{n}}{equation}
popularized by Ap\'ery and Lehmer is evaluated for positive integers $k$ along
with the asymptotic behavior for large $k$. It is found that value $z=2$, as
commented on by D. H. Lehmer provides a unique relation to $\pi$.

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