On generalized degenerate Gould-Hopper based fully degenerate Bell polynomials

Volume 21, Issue 3, pp 243--257 http://dx.doi.org/10.22436/jmcs.021.03.07

Publication Date: April 27, 2020 Submission Date: January 15, 2020 Revision Date: February 09, 2020 Accteptance Date: March 03, 2020

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Authors

Ugur Duran - Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, TR-31200 Hatay, Turkey. Mehmet Acikgoz - Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, TR-27310 Gaziantep, Turkey.

Abstract

In this paper, we introduce both the generalized degenerate Gould-Hopper based degenerate Stirling polynomials of the second kind and the generalized degenerate Gould-Hopper based fully degenerate Bell polynomials. We study and investigate multifarious properties and relations of these polynomials such as explicit formulas, differentiation rules and summation formulas. Moreover, we derive several correlations with the degenerate Bernstein polynomials for these polynomials. Furthermore, we acquire several representations of the generalized degenerate Gould-Hopper based fully degenerate Bell polynomials via not only the fully degenerate Bell polynomials but also the generalized degenerate Gould-Hopper based degenerate Bernoulli, Euler and Genocchi polynomials.

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Keywords

• Degenerate exponential function
• Bell polynomials
• Gould-Hopper polynomials
• Bernstein polynomials
• Stirling numbers of the second kind

MSC

•  11B73
•  11B68
•  11B83
•  33B10

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