2004/02/29 by David M. Bradley · 2 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical functions and polynomials #math.CO #math.NT #msc:05A30 #msc:33D15
paper · pdf · doi:10.1016/j.disc.2005.06.008
published as Discrete Mathematics, 300 (2005), no. 1--3, pp. 44--56. MR2170113 (2006m:05019) · 12 pages AMSLaTeX. Submitted for publication October 26, 2003; revised September 14, 2004. New title reflects change in emphasis and new section devoted to connections with inverse pairs and Hoffman duality. References added and typos corrected
arxiv created 2004/09/22 · openalex publication_date 2005/08/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial coefficients. Special cases of these identities--for example, with all parameters equal to 1--have occurred in the literature. The special case with only one parameter reduces to an identity for the divisor generating function, which has received some attention in connection with problems in sorting theory. The general case can be viewed as a duality result, reminiscent of the duality relation for the ordinary multiple zeta function.