Some Families of q-Sums and q-Products

Abstract

In this paper, we introduce two new binary operations, the one called q-sum and defined on the set of all real numbers and the other called q-product and defined on a subset of real numbers, which have potential importance in the study of q-numbers. The set of q-numbers of all real numbers, for example, is a field when these operations are restricted to it. Also, we introduce new q-exponential and q-logarithm and show some relations for them. Finally, we give some remarks on the well-known q-gamma, q-exponential, and q-beta functions.