Partial Euler Product Dirichlet Series Analogues Of q-Series

Mathematics Research Report MRR95-083

Partial Euler Product Dirichlet Series Analogues Of q-Series

Geoffrey B. Campbell

Abstract: In prequels [2,4] we examined a new class of Dirichlet series based on known q-series identities. The new D-analogues, as they were termed, came from applying an Euler product operator over all primes. In the current paper we show that with a partial product in the operator, the same rationale will lead to yet another set of D-analogues from the same q-series under transform as previously used in the earlier two papers. Similar summations are given as analogues for the q-Gauss, q-Kummer, and the q-Dixon sums.

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