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Open AccessArticle

Certain Results for the Twice-Iterated 2D q-Appell Polynomials

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Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Department of Applied Mathematics, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India
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Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1307; https://doi.org/10.3390/sym11101307
Received: 16 September 2019 / Revised: 10 October 2019 / Accepted: 12 October 2019 / Published: 16 October 2019
(This article belongs to the Special Issue Polynomials: Special Polynomials and Number-Theoretical Applications)
In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated. View Full-Text
Keywords: 2D q-Appell polynomials; twice-iterated 2D q-Appell polynomials; determinant expressions; recurrence relations; 2D q-Bernoulli polynomials; 2D q-Euler polynomials; 2D q-Genocchi polynomials; Apostol type Bernoulli; Euler and Genocchi polynomials 2D q-Appell polynomials; twice-iterated 2D q-Appell polynomials; determinant expressions; recurrence relations; 2D q-Bernoulli polynomials; 2D q-Euler polynomials; 2D q-Genocchi polynomials; Apostol type Bernoulli; Euler and Genocchi polynomials
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Srivastava, H.M.; Yasmin, G.; Muhyi, A.; Araci, S. Certain Results for the Twice-Iterated 2D q-Appell Polynomials. Symmetry 2019, 11, 1307.

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