Duality of one-variable multiple polylogarithms and their $q$-analogues

Abstract

The duality relation of one-variable multiple polylogarithms was proved by Hirose, Iwaki, Sato and Tasaka by means of iterated integrals. In this paper, we give a new proof using the method of connected sums, which was recently invented by Seki and the author. Interestingly, the connected sum involves the hypergeometric function in its connector. Moreover, we introduce two kinds of $q$-analogues of the one-variable multiple polylogarithms and generalize the duality to them.

10 pages; some typos are fixed; to appear in Tokyo Journal of Mathematics

References in corpus (1)

• Multiple $q$-Zeta Values

Cited by in corpus (1)

• Connectors of the Ohno relation for parametrized multiple zeta series