A $q$-analogue of the Koecher-Leshchiner generating function of odd zeta values

Roberto Tauraso

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arXiv · 2511.18034

A $q$-analogue of the Koecher-Leshchiner generating function of odd zeta values

Roberto Tauraso

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Abstract

In the 1980s, Koecher and, independently, Leshchiner found an elegant formula for the generating function of odd zeta values. In this short note, we derive a $q$-analogue of this formula, which provides a $q$-version of the accelerated series for $\zeta(3)$ used by Ap\'ery in his famous proof of irrationality.

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Roberto Tauraso. 2025-11-22. A $q$-analogue of the Koecher-Leshchiner generating function of odd zeta values. https://arxiv.org/abs/2511.18034

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