Gauss hypergeometric functions, multiple polylogarithms, and multiple zeta values
The author employs the theory of the formal KZ equation to obtain an analytic iterated integral expression of the Gauss hypergeometric functions by viewing the hypergeometric equation as a representation of the formal KZ equation. This result yields an expression for the generating function of the multiple polylogarithms of one variable of fixed weight, depth, and height (see the work of \textit{Y. Ohno} and \textit{D. Zagier} [Indag. Math., New Ser. 12, No.4, 483--487 (2001; Zbl 1031.11053)]) in terms of iterated integrals. Following this, the author recovers functional equations for multiple polylogarithms and, after specializing, relations for multiple zeta values including Euler's inversion formula and others.
scientific article; zbMATH DE number 5673112
scientific article