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S. Araci, M. Acikgoz, A. Bagdasaryan, E. Sen, The Legendre Polynomials Associated with Bernoulli, Euler, Hermite and Bernstein Polynomials, Turkish J. Anal. Number Theory, Vol. 1, No. 1, (2013) 1-3.

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Article

New Extensions of Some Known Special Polynomials under the Theory of Multiple q-Calculus

1Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, Gaziantep, Turkey

2Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, Gaziantep, Turkey


Turkish Journal of Analysis and Number Theory. 2015, Vol. 3 No. 5, 128-139
DOI: 10.12691/tjant-3-5-4
Copyright © 2015 Science and Education Publishing

Cite this paper:
Mehmet Acikgoz, Serkan Araci, Uğur Duran. New Extensions of Some Known Special Polynomials under the Theory of Multiple q-Calculus. Turkish Journal of Analysis and Number Theory. 2015; 3(5):128-139. doi: 10.12691/tjant-3-5-4.

Correspondence to: Serkan  Araci, Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, Gaziantep, Turkey. Email: mtsrkn@hotmail.com

Abstract

In the year 2014, the idea of multiple q-calculus was formulated and introduced in the book of Nalci and Pashaev [9] in which this idea is simple but elegant method in order to derive new generating functions of some special polynomials that are generalizations of known q-polynomials. In this paper, we will use Nalci and Pashaev’s method in order to find a systematic study of new types of the Bernoulli polynomials, Euler polynomials and Genocchi polynomials. Also we will obtain recursive formulas for these polynomials.

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