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

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

2004-05-10

arxiv.org/abs/math/0405162v2

Mathematics

Number Theory

Scientific paper

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.

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