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arXiv · 2507.19793

Truncated Hypergeometric Functions and Discretized Integrals

Shuji Yamamoto
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Abstract

We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between truncated series and discretized integrals which comes from the mutliple zeta values and multiple polylogarithms. We also prove the formula of Ohno-Zagier type which relates the truncated multiple polylogarithms and the truncated hypergeometric series.

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Shuji Yamamoto. 2025-07-26. Truncated Hypergeometric Functions and Discretized Integrals. https://arxiv.org/abs/2507.19793

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