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

2025/11/22 by Tauraso, Roberto
#05A15 #05A19 #05A30 #11B65 #11M06 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.18034

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 ζ(3) used by Apéry in his famous proof of irrationality.

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