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Mathematics 2019, 7(2), 121; https://doi.org/10.3390/math7020121

On Gould–Hopper-Based Fully Degenerate Poly-Bernoulli Polynomials with a q-Parameter

1
Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, TR-31200 Hatay, Turkey
2
Faculty of Industrial Engineering, University of Douala, Douala B.P. 2701, Cameroon
*
Author to whom correspondence should be addressed.
Received: 27 November 2018 / Revised: 17 January 2019 / Accepted: 20 January 2019 / Published: 23 January 2019
(This article belongs to the Special Issue Special Polynomials)
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Abstract

We firstly consider the fully degenerate Gould–Hopper polynomials with a q parameter and investigate some of their properties including difference rule, inversion formula and addition formula. We then introduce the Gould–Hopper-based fully degenerate poly-Bernoulli polynomials with a q parameter and provide some of their diverse basic identities and properties including not only addition property, but also difference rule properties. By the same way of mentioned polynomials, we define the Gould–Hopper-based fully degenerate ( α , q ) -Stirling polynomials of the second kind, and then give many relations. Moreover, we derive multifarious correlations and identities for foregoing polynomials and numbers, including recurrence relations and implicit summation formulas. View Full-Text
Keywords: Gould–Hopper polynomials; Bernoulli polynomials; Hermite polynomials; poly Bernoulli polynomials; Stirling numbers of second kind; Polylogarithm functions; Cauchy product Gould–Hopper polynomials; Bernoulli polynomials; Hermite polynomials; poly Bernoulli polynomials; Stirling numbers of second kind; Polylogarithm functions; Cauchy product
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 (CC BY 4.0).
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Duran, U.; Sadjang, P.N. On Gould–Hopper-Based Fully Degenerate Poly-Bernoulli Polynomials with a q-Parameter. Mathematics 2019, 7, 121.

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