Gauss hypergeometric functions, multiple polylogarithms, and multiple zeta values
type: Item
instance of: scholarly article
title: Gauss hypergeometric functions, multiple polylogarithms, and multiple zeta values
zbMATH Open document ID: 1188.33009
author: Shu Oi
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2010-02-19T00:00:00Z
review text: 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.
reviewed by: Matilde Lalín
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 11M32
Mathematics Subject Classification ID: 33B30
zbMATH DE Number: 5673112
zbMATH Keywords: KZ equation
zbMATH Keywords: Gauss hypergeometric functions
zbMATH Keywords: multiple polylogarithms
zbMATH Keywords: multiple zeta values
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1260476650
OpenAlex ID: W2162572910
cites work: Theory of Hypergeometric Functions
cites work: Special values of multiple polylogarithms
cites work: Q5443951
cites work: Q3351551
cites work: Derivation and double shuffle relations for multiple zeta values
cites work: Q5820777
cites work: Q4001952
cites work: Q4232510
cites work: DUALITY FORMULAS OF THE SPECIAL VALUES OF MULTIPLE POLYLOGARITHMS
cites work: The Sum Formula for Multiple Zeta Values and Connection Problem of the Formal Knizhnik-Zamolodchikov Equation
cites work: Relations for multiple zeta values and Mellin transforms of multiple polylogarithms
cites work: Multiple zeta values of fixed weight, depth, and height
cites work: Q3134850
cites work: Q4324348
DOI: 10.2977/PRIMS/1260476650
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description: scientific article; zbMATH DE number 5673112