JournalsprimsVol. 45, No. 4pp. 981–1009

Gauss Hypergeometric Functions, Multiple Polylogarithms, and Multiple Zeta Values

  • Shu Oi

    Waseda University, Tokyo, Japan
Gauss Hypergeometric Functions, Multiple Polylogarithms, and Multiple Zeta Values cover
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Abstract

In this article, we express solutions of the Gauss hypergeometric equation as a series of the multiple polylogarithms by using iterated integral. This representation is the most simple case of a semisimple representation of solutions of the formal KZ equation. Moreover, combining this representation with the connection relations of solutions of the Gauss hypergeometric equation, we obtain various relations of the multiple polylogarithms of one variable and the multiple zeta values.

Cite this article

Shu Oi, Gauss Hypergeometric Functions, Multiple Polylogarithms, and Multiple Zeta Values. Publ. Res. Inst. Math. Sci. 45 (2009), no. 4, pp. 981–1009

DOI 10.2977/PRIMS/1260476650