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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71114We 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.Number TheoryClassical Analysis and ODEsQuantum Algebra11M06; 40B05; 33C05Representation of the Gauss hypergeometric function by multiple polylogarithms and relations of multiple zeta valuestext