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

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 ${}_3{F}_2$. 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.

12 pages