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Generating function of multiple polylog of Hurwitz type

Published online by Cambridge University Press:  21 November 2022

Kentaro Ihara*
Faculty of Science and Engineering, Kindai University, 3-4-1 Kowakae, Higashi-Osaka, Japan
Yusuke Kusunoki
EX Corporation, 3-19-3 Toyosaki, Osaka, Japan e-mail:
Yayoi Nakamura
Faculty of Science and Engineering, Kindai University, 3-4-1 Kowakae, Higashi-Osaka, Japan e-mail:
Hitomi Saeki
Uenomiya Taishi Senior High School, Minamikawachi, Osaka, Japan e-mail:


We introduce interpolated multiple Hurwitz polylogs and interpolated multiple Hurwitz zeta values. In addition, we discuss the generating functions for the sum of the polylogs/zeta values of fixed weight, depth, and all heights. The functions are expressed in terms of generalized hypergeometric functions. Compared with the pioneering results of Ohno and Zagier on the generating function, our setup generalizes the results in three directions, namely, at general heights, with a t-interpolation, and as a Hurwitz type. As an application, by fixing the Hurwitz parameter to rational numbers, the generating functions for multiple zeta values with level are given.

© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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The first author is supported by JSPS KAKENHI Grant Number 18K03260.


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