Geodesic
Generating function of multiple polylog of Hurwitz type
Canadian journal of mathematics, Tome 76 (2024) no. 1, pp. 1-17

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DOI

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.
DOI : 10.4153/S0008414X22000621
Mots-clés : Multiple zeta values, Hurwitz zeta function, hypergeometric functions 
Ihara, Kentaro; Kusunoki, Yusuke; Nakamura, Yayoi; Saeki, Hitomi. Generating function of multiple polylog of Hurwitz type. Canadian journal of mathematics, Tome 76 (2024) no. 1, pp. 1-17. doi: 10.4153/S0008414X22000621
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     title = {Generating function of multiple polylog of {Hurwitz} type},
     journal = {Canadian journal of mathematics},
     pages = {1--17},
     year = {2024},
     volume = {76},
     number = {1},
     doi = {10.4153/S0008414X22000621},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000621/}
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