A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral ${}_2H_2$ summation

Takumi Maesaka; Masataka Ono

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arXiv · 2610.17957

A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral ${}_2H_2$ summation

Takumi Maesaka·Masataka Ono

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Abstract

We establish a generating function identity for finite and symmetric multiple zeta values using Dougall's bilateral ${}_2H_2$ summation formula. As an application, we prove a restricted sum formula in which the parity of each component of the index is prescribed. We also derive a generating function identity for finite multiple zeta values $ζ^{}_{\mathcal{A}}(\{1,2\}^n)$ and symmetric multiple zeta values $ζ^{}_{\mathcal{S}}(\{1,2\}^n)$, thereby proving Kaneko's conjecture for finite multiple zeta values and its symmetric analogue.

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BibTeX RIS

Takumi Maesaka, Masataka Ono. 2026-10-13. A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral ${}_2H_2$ summation. https://arxiv.org/abs/2610.17957

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