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

Source 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.