Generalized Gould-Hopper Based Fully Degenerate Central Bell Polynomials

Ugur Duran^1, and Mehmet Acikgoz²

¹Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences,·Iskenderun Technical University, TR-31200 Hatay, Turkey

²University of Gaziantep, Faculty of Science and Arts, Department of Mathematics, TR-27310 Gaziantep, Turkey

Cite this paper:
Ugur Duran and Mehmet Acikgoz. Generalized Gould-Hopper Based Fully Degenerate Central Bell Polynomials. Turkish Journal of Analysis and Number Theory. 2019; 7(5):124-134. doi: 10.12691/tjant-7-5-1

Abstract

In this paper, we first provide the generalized degenerate Gould-Hopper polynomials via the degenerate exponential functions and then give various relations and formulas such as addition formula and explicit identity. Moreover, we consider the generalized Gould-Hopper based degenerate central factorial numbers of the second kind and present several identities and relationships. Furthermore, we introduce the generalized Gould-Hopper based fully degenerate central Bell polynomials and investigated multifarious correlations and formulas including summation formulas, derivation rule and correlations with the Stirling numbers of the first kind, the generalized Gould-Hopper based degenerate central factorial numbers of the second kind and the generalized degenerate Gould-Hopper polynomials. We then acquire some relations with the degenerate Bernstein polynomials for the generalized Gould-Hopper based fully degenerate central Bell polynomials. Finally, we consider the Gould-Hopper based fully degenerate Bernoulli, Euler and Genocchi polynomials and by utilizing these polynomials, we develop some representations for the generalized Gould-Hopper based fully degenerate central Bell polynomials.

Keywords:
Degenerate exponential function Central factorial numbers Central Bell polynomials Gould-Hopper polynomials Stirling numbers of the first kind

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