International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 21, Pages 3453-3458
doi:10.1155/IJMMS.2005.3453

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

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.