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

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 $\mathbb{Z}$ 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.