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arXiv · 2505.08935

On the $p$-adic valuations of values of Legendre polynomials

Max A. Alekseyev·Tewodros Amdeberhan·Jeffrey Shallit·Ingrid Vukusic
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Abstract

We prove an explicit formula for the $p$-adic valuation of the Legendre polynomials $P_n(x)$ evaluated at a prime $p$, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017.

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Max A. Alekseyev, Tewodros Amdeberhan, Jeffrey Shallit, Ingrid Vukusic. 2025-05-13. On the $p$-adic valuations of values of Legendre polynomials. https://arxiv.org/abs/2505.08935

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