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arXiv · 1012.3833

Congruences concerning Legendre polynomials

Zhi-Hong Sun
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Abstract

Let $p$ be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for $\sum_{k=0}^{\frac{p-1}2}\binom{2k}k^2m^{-k}\mod {p^2}$. In particular, we confirm several conjectures of Z.W. Sun. We also pose 13 conjectures on supercongruences.

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Zhi-Hong Sun. 2010-12-17. Congruences concerning Legendre polynomials. https://doi.org/10.1090/s0002-9939-2010-10566-x

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