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

Authors

AHMED SALEM
FARUK UÇAR

DOI

10.3906/mat-1411-70

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

First Page

98

Last Page

107

Recommended Citation

SALEM, AHMED and UÇAR, FARUK (2016) "The $q$-analogue of the $E_{2;1}$-transform and its applications," Turkish Journal of Mathematics: Vol. 40: No. 1, Article 9. https://doi.org/10.3906/mat-1411-70
Available at: https://journals.tubitak.gov.tr/math/vol40/iss1/9