JournalsprimsVol. 40, No. 2pp. 537–564

Relations for Multiple Zeta Values and Mellin Transforms of Multiple Polylogarithms

  • Jun-ichi Okuda

    Waseda University, Tokyo, Japan
  • Kimio Ueno

    Waseda University, Tokyo, Japan
Relations for Multiple Zeta Values and Mellin Transforms of Multiple Polylogarithms cover
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Abstract

In this paper a relationship between the Ohno relation for multiple zeta values and multiple polylogarithms are discussed. First we introduce generating functions for the Ohno relation, and investigate their properties. We show that there exists a subfamily of the Ohno relation which recovers algebraically its totality. This is proved through analysis of Mellin transform of multiple polylogarithms. Furthermore, this subfamily is shown to be converted to the Landen connection formula for multiple polylogarithms by inverse Mellin transform.

Cite this article

Jun-ichi Okuda, Kimio Ueno, Relations for Multiple Zeta Values and Mellin Transforms of Multiple Polylogarithms. Publ. Res. Inst. Math. Sci. 40 (2004), no. 2, pp. 537–564

DOI 10.2977/PRIMS/1145475814