A q -analog of Euler's decomposition formula for the double zeta function

David M. Bradley

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-6

Abstract:

The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler's results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum of double zeta values involving binomial coefficients. Here, we establish a q -analog of Euler's decomposition formula. More specifically, we show that Euler's decomposition formula can be extended to what might be referred to as a “double q -zeta function” in such a way that Euler's formula is recovered in the limit as q tends to 1.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:120295

DOI: 10.1155/IJMMS.2005.3453

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