Ohno-Zagier type relation for multiple $t$-values

TL;DR

This paper explores Ohno-Zagier type relations for multiple t-values and their star variants, expressing generating functions via hypergeometric functions and deriving new sum formulas for fixed weight and depth.

Contribution

It introduces a novel representation of generating functions for multiple t-values using hypergeometric functions and derives new sum formulas for fixed weight, depth, and height.

Findings

Generated explicit formulas for sums of multiple t-values.

Expressed generating functions in terms of hypergeometric functions.

Derived weighted sum formulas for fixed weight and depth.

Abstract

We study the Ohno-Zagier type relation for multiple $t$-values and multiple $t$-star values. We represent the generating function of sums of multiple $t$-(star) values with fixed weight, depth and height in terms of the generalized hypergeometric function $\,_3F_2$. As applications, we get a formula for the generating function of sums of multiple $t$-(star) values of maximal height and a weighted sum formula for sums of multiple $t$-(star) values with fixed weight and depth.