# Generating functions for Ohno type sums of finite and symmetric multiple zeta-star values

## TL;DR

This paper confirms a conjecture about generating functions for Ohno type sums of finite and symmetric multiple zeta-star values, providing explicit formulas for depth three indices, advancing understanding of these special sums.

## Contribution

It proves Kaneko's conjecture on the generating function for a specific depth three index and extends the formula to arbitrary depth three indices.

## Key findings

- Confirmed Kaneko's conjecture on generating functions.
- Derived explicit formulas for depth three indices.
- Enhanced understanding of Ohno type sums of multiple zeta-star values.

## Abstract

Ohno's relation states that a certain sum, which we call an Ohno type sum, of multiple zeta values remains unchanged if we replace the base index by its dual index. In view of Oyama's theorem concerning Ohno type sums of finite and symmetric multiple zeta values, Kaneko looked at Ohno type sums of finite and symmetric multiple zeta-star values and made a conjecture on the generating function for a specific index of depth three. In this paper, we confirm this conjecture and further give a formula for arbitrary indices of depth three.