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arXiv · 2401.09562

On an identity by Ercolani, Lega, and Tippings

Maxim L. Yattselev
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Abstract

In this note we prove that \[ j!\,2^N \, \binom{N+j-1}{j} \, {}_2F_1\left(\begin{matrix}-j,-2j \\ -N-j+1 \end{matrix};-1\right) = \sum_{l=0}^N \binom{N}{l}\prod_{i=0}^{j-1}2(2i+1+l), \] where $ N $ and $ j $ are positive integers, which resolves a question posed by Ercolani, Lega, and Tippings.

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Maxim L. Yattselev. 2024-01-17. On an identity by Ercolani, Lega, and Tippings. https://arxiv.org/abs/2401.09562

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