The qq-analogue of the E2;1E2;1-transform and its applications

Abstract

In this paper, we introduce a new integral transform qE2;1 , which is the q -analogue of the E2;1 -transform and can be regarded as a q -extension of the E2;1 -transform. Some identities involving qL2 -transfom, qL2 -transfom, and Pq -transform are given. By making use of these identities and qE2;1 -transform, a new Parseval Goldstein type theorem is obtained. Some examples are also given as an illustration of the main results presented here.