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

Mehmet Acikgoz¹, Serkan Araci^2, and Uğur Duran¹

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

Cite this paper:
Mehmet Acikgoz, Serkan Araci and 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

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.

Keywords:
Quantum calculus Multiple quantum calculus q-Bernoulli polynomials q-Euler polynomials q-Genocchi polynomials Generating function

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