More congruences from Apery-like formulae

Abstract

We present some congruences modulo $p^{6-d}$ for sums of the type ${\sum }_{k=0}^{(p-3)/2}{x}^k\left(\genfrac{}{}{0ex}{}{2k}{k}\right)/(2k+1{)}^d$, for $d=1,2,3$ where $p>5$ is a prime.

This is a preliminary draft and more refined versions will follow

References in corpus (1)

• Congruences arising from Apéry-type series for zeta values

Cited by in corpus (1)

• p-adic congruences motivated by series