An Euler product transform applied to q-series |
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| Authors: | Geoffrey B. Campbell |
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| Affiliation: | (1) Department of Mathematics, La Trobe University, Bundoora, Victoria, 3086, Australia |
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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. 2000 Mathematics Subject Classification Primary—11M41; Secondary—33D15, 30B50 |
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| Keywords: | Dirichlet series and zeta functions Basic hypergeometric functions in one variable Dirichlet series and other series expansions Exponential series |
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