On the Sum Formula for Multiple $q$-Zeta Values
نویسندگان
چکیده
منابع مشابه
ON THE SUM FORMULA FOR MULTIPLE q-ZETA VALUES
Abstract. Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q → 1. Here, we discuss the sum formula for multiple q-zeta values, and provide a self-contained proof. As a consequence, we also derive a q-analog of Euler’s ...
متن کاملWeighted Sum Formula for Multiple Zeta Values
Abstract. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler’s formula was o...
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In this article, the q-analogues of the linear relations of non-strict multiple zeta values called “the sum formula” and “the cyclic sum formula” are established.
متن کاملSUM OF MULTIPLE q-ZETA VALUES
The generating function of the sums of multiple q-zeta values with fixed weights, depths and 1-heights, 2-heights, . . . , r-heights is represented in terms of specializations of basic hypergeometric functions.
متن کاملMultiple q-zeta values
We introduce a q-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple q-zeta values satisfy a q-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values. Additionally, multiple q-zeta values can be viewed as special values of the multiple q-polylogarithm, which ad...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2007
ISSN: 0035-7596
DOI: 10.1216/rmjm/1194275927