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arXiv · 0912.2497

New harmonic number identities with applications

Roberto Tauraso
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Abstract

We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{λ_j})$ when $\sum_{j=1}^r λ_j\leq 5$. We apply these identities to the study of two congruences modulo a power of a prime.

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Roberto Tauraso. 2009-12-13. New harmonic number identities with applications. https://arxiv.org/abs/0912.2497

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