Generating Function of q- and Elliptic Multiple Polylogarithms of Hurwitz Type

Abstract Ohno and Zagier (Indag Math 12: 483–487, 2001) found that a generating function of sums of multiple polylogarithms can be written in terms of the Gauss hypergeometric function ₂F₁ 2 F 1. As a generalization of the Ohno and Zagier formula, Ihara et al. (Can J Math 76: 1–17, 2022) showed that a generating function of sums of interpolated multiple polylogarithms of Hurwitz type can be expressed in terms of the generalized hypergeometric function ₑ+₁Fᵣ r + 1 F r. In this paper, we establish q - and elliptic analogues of this result. We introduce elliptic q -multiple polylogarithms of Hurwitz type and study a generating function of sums of them. By taking the trigonometric and classical limits in the main theorem, we can obtain q - and elliptic generalizations of the Ihara, Kusunoki, Nakamura and Saeki formula.