The $q$-analogue of the $E_{2;1}$-transform and its applications

Authors: AHMED SALEM, FARUK UÇAR

Abstract: In this paper, we introduce a new integral transform $\ _{q}\mathcal{E}_{2;1}$, which is the $q$-analogue of the $\mathcal{E}_{2;1}$-transform and can be regarded as a $\mathit{q}$-extension of the $\mathcal{E}_{2;1}$-transform. Some identities involving $~_{q}L_{2}$-transfom, $~_{q}\mathcal{L}_{2}$-transfom, and $\mathcal{P}_{q}$-transform are given. By making use of these identities and $\ _{q}\mathcal{E}_{2;1}$-transform, a new Parseval--Goldstein type theorem is obtained. Some examples are also given as an illustration of the main results presented here.

Keywords: $q$-Exponential integral, $_{q}L_{2}$-transfom, $_{q}\mathcal{L}_{2}$-transfom, $\mathcal{P}_{q}$-transform, $q$-analogue of $\mathcal{E}_{2;1}$-transform

Full Text: PDF