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Apostol Type (p, q)-Frobenius-Euler Polynomials and Numbers
Version 1
: Received: 14 December 2017 / Approved: 15 December 2017 / Online: 15 December 2017 (09:14:10 CET)
How to cite: Duran, U.; Acikgoz, M. Apostol Type (p, q)-Frobenius-Euler Polynomials and Numbers. Preprints 2017, 2017120104. https://doi.org/10.20944/preprints201712.0104.v1 Duran, U.; Acikgoz, M. Apostol Type (p, q)-Frobenius-Euler Polynomials and Numbers. Preprints 2017, 2017120104. https://doi.org/10.20944/preprints201712.0104.v1
Abstract
In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].
Keywords
(p, q)-calculus; Bernoulli polynomials; Euler polynomials; Genocchi polynomials; Frobenius-Euler polynomials; generating function; Cauchy product
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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