A q ‐analog of Euler′s decomposition formula forthe double zeta function

Source 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.