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

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  • David M. Bradley

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.

Suggested Citation

  • David M. Bradley, 2005. "A q -analog of Euler's decomposition formula for the double zeta function," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:120295
    DOI: 10.1155/IJMMS.2005.3453
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