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Certain Results of q -Sheffer–Appell Polynomials

Department of Applied Mathematics, Aligarh Muslim University, Aligarh 202002, India
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(2), 159;
Received: 12 December 2018 / Revised: 24 January 2019 / Accepted: 28 January 2019 / Published: 1 February 2019
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
PDF [558 KB, uploaded 1 February 2019]


In this paper, the class of q -Sheffer–Appell polynomials is introduced. The generating function, series definition, determinant definition and some other identities of this class are established. Certain members of q -Sheffer–Appell polynomials are investigated and some properties of these members are derived. In addition, the class of 2D q -Sheffer–Appell polynomials is introduced. Further, the graphs of some members of q -Sheffer–Appell polynomials and 2D q -Sheffer–Appell polynomials are plotted for different values of indices by using Matlab. View Full-Text
Keywords: q -Sheffer–Appell polynomials; generating relations; determinant definition; recurrence relation; q -Hermite–Bernoulli polynomials; q -Hermite–Euler polynomials; q -Hermite–Genocchi polynomials q -Sheffer–Appell polynomials; generating relations; determinant definition; recurrence relation; q -Hermite–Bernoulli polynomials; q -Hermite–Euler polynomials; q -Hermite–Genocchi polynomials

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Yasmin, G.; Muhyi, A.; Araci, S. Certain Results of q -Sheffer–Appell Polynomials. Symmetry 2019, 11, 159.

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