Abstract
The double zeta function is a function of two arguments defined by a double Dirichlet series and was first studied by Euler in response to a letter from Goldbach in 1742. By calculating many examples, Euler inferred a closed-form evaluation of the double zeta function in terms of values of the Riemann zeta function, in the case when the two arguments are positive integers with opposite parity. Here, we establish a q-analog of Euler’s evaluation. That is, we state and prove a 1-parameter generalization that reduces to Euler’s evaluation in the limit as the parameter q tends to 1.
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Communicated by Heinz H. Bauschke.
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Bradley, D.M., Zhou, X. (2013). A q-Analog of Euler’s Reduction Formula for the Double Zeta Function. In: Bailey, D., et al. Computational and Analytical Mathematics. Springer Proceedings in Mathematics & Statistics, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7621-4_7
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DOI: https://doi.org/10.1007/978-1-4614-7621-4_7
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