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Article
The $q$-analogue of the $E_{2;1}$-transform and its applications
Turkish Journal of Mathematics
Disciplines
Publication Date
1-1-2016
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
Citation Information
AHMED SALEM and FARUK UÇAR. "The $q$-analogue of the $E_{2;1}$-transform and its applications" Vol. 40 Iss. 1 (2016) p. 98 - 107 Available at: http://works.bepress.com/ahmed-salem/17/