A 𝑞-analogue of non-strict multiple zeta values and basic hypergeometric series

Takeyama, Yoshihiro

doi:10.1090/S0002-9939-09-09931-6

A $q$-analogue of non-strict multiple zeta values and basic hypergeometric series
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Proc. Amer. Math. Soc. 137 (2009), 2997-3002 Request permission

Abstract:

We consider the generating function for a $q$-analogue of non-strict multiple zeta values (or multiple zeta-star values) and prove an explicit formula for it in terms of a basic hypergeometric series ${}_{3}\phi _{2}$. By specializing the variables in the generating function, we reproduce the sum formula obtained by Ohno and Okuda and get some relations in the case of full height.

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