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

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英文摘要

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.

作者：Max A. Alekseyev、Tewodros Amdeberhan、Jeffrey Shallit、Ingrid Vukusic

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学科分类：数学

推荐引用：Max A. Alekseyev,Tewodros Amdeberhan,Jeffrey Shallit,Ingrid Vukusic.On the $p$-adic valuations of values of Legendre polynomials[EB/OL].(2025-05-13)[2025-07-16].https://arxiv.org/abs/2505.08935.点此复制

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

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

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