Dirichlet series analogues of q-series

Research Report MRR00-014

Dirichlet series analogues of q-series

Geoffrey B. Campbell

Abstract: This paper introduces a new concept into mathematical analysis, that 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 basic hypergeometric series, whilst widely used in mathematics, is itself an analogue for the ordinary hypergeometric series developed by Gauss in the early nineteenth century. We present a variety of results that are demonstrably analogues of many classical formulae from the theories of ordinary and basic hypergeometric series.

This service is maintained by the Mathematical Sciences Institute (MSI)
Comments to webmaster@maths.anu.edu.au URL: http://wwwmaths.anu.edu.au/