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

Shu Oi

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arXiv · math/0405162

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

Shu Oi

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Abstract

We describe a solution of the Gauss hypergeometric equation, $F(α,β,γ;z)$ by power series in paramaters $α,β,γ$ 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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Shu Oi. 2004-06-11. Representation of the Gauss hypergeometric function by multiple polylogarithms and relations of multiple zeta values. https://arxiv.org/abs/math/0405162

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