Representation of the Gauss hypergeometric function by multiple polylogarithms and relations of multiple zeta values

Shu Oi

Published 2004-05-10, updated 2004-06-11Version 2

We describe a solution of the Gauss hypergeometric equation, $F(\alpha,\beta,\gamma;z)$ by power series in paramaters $\alpha,\beta,\gamma$ whose coefficients are $\Z$ linear combinations of multiple polylogarithms. And using the representation and connection reletions of solutions of the hypergeometric equation, we show some relations of multiple zeta values.