2005/01/01 by David M. Bradley · 2 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical Inequalities and Applications #math.NT #msc:11M41
paper · pdf · doi:10.1155/ijmms.2005.3453
published as International Journal of Mathematics and Mathematical Sciences, 2005:21 (2005), pp. 3453--3458. MR2206867 (2006k:11174) · 6 pages
openalex publication_date 2005/01/01 · arxiv created 2005/01/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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.