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

Abstract

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.

References in corpus (1)

• Duality formulas of the Special Values of Multiple Polylogarithms

Cited by in corpus (4)

• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• All order epsilon-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
• Square lattice Ising model susceptibility: Series expansion method and differential equation for ${\chi }^{(3)}$