The q-Dixon sum Dirichlet series analogue

TL;DR

This paper introduces a Dirichlet series analogue of the q-Dixon sum, providing a new perspective on hypergeometric q-series and their classical counterparts, and compares it with existing Dixon theorems.

Contribution

It presents the first Dirichlet series analogue of the q-Dixon sum, bridging classical, q-analogue, and D-analogue hypergeometric series.

Findings

Defined the D-analogue of the q-Dixon sum

Established a direct comparison with classical Dixon theorem

Extended the framework of hypergeometric series analogues

Abstract

A few years ago, the concept of a D-analogue was introduced as a Dirichlet series analogue for the already known and well researched hypergeometric q-series. The D-analogue of the q-Dixon sum is given here, in the context of seeing a direct comparison with the old Dixon theorem and the q-analogue.