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arXiv · 2510.25059

A $q$-analogue of Boyadzhiev-Mneimneh-type binomial sums of finite multi-polylogarithms

Ken Kamano
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Abstract

We give a formula for a $q$-analogue of Boyadzhiev-Mneimneh-type binomial sums of finite multi-polylogarithms. In the limit as $q\to 1$, this formula reduces to an identity equivalent to the Sakugawa-Seki identities. We also give a formula for Boyadzhiev-Mneimneh-type sums corresponding to the Cauchy binomial theorem.

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Ken Kamano. 2025-10-29. A $q$-analogue of Boyadzhiev-Mneimneh-type binomial sums of finite multi-polylogarithms. https://arxiv.org/abs/2510.25059

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