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arXiv · 1108.1893

Congruences arising from Ap\'ery-type series for zeta values

Khodabakhsh Hessami Pilehrood·Tatiana Hessami Pilehrood
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Abstract

Recently, R. Tauraso established finite $p$-analogues of famous Ap\'ery series for $\zeta(2)$ and $\zeta(3).$ In this paper, we present several congruences for finite central binomial sums arising from the truncation of Ap\'ery-type series for $\zeta(4)$ and $\zeta(5).$ We also prove a $p$-analogue of Zeilberger's series for $\zeta(2)$ confirming a conjecture of Z. W. Sun.

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Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood. 2011-08-09. Congruences arising from Ap\'ery-type series for zeta values. https://doi.org/10.1016/j.aam.2012.05.003

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