The Ramanujan Journal

, Volume 12, Issue 2, pp 267–293 | Cite as

An Euler product transform applied to q-series

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Abstract

This paper introduces the concept of a D-analogue. This is a Dirichlet series analogue for the already known and well researched hypergeometric q-series, often called the basic hypergeometric series. The main result in this paper is a transform, based on an Euler product over the primes. Examples given are D-analogues of the q-binomial theorem and the q-Gauss summation.

Keywords

Dirichlet series and zeta functions Basic hypergeometric functions in one variable Dirichlet series and other series expansions Exponential series 
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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of MathematicsLa Trobe UniversityBundooraAustralia

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