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

David M. Bradley
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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. In this note, 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.

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David M. Bradley. 2005-01-31. A q-analog of Euler's decomposition formula for the double zeta function. https://doi.org/10.1155/ijmms.2005.3453

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