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Volume 14
Issue 8
10.3390/sym14081500
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Article

Analytical Properties of Degenerate Genocchi Polynomials of the Second Kind and Some of Their Applications

by
Waseem Ahmad Khan
1,* and
Maryam Salem Alatawi
2
1
Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
2
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2022, 14(8), 1500; https://doi.org/10.3390/sym14081500
Submission received: 28 June 2022 / Revised: 14 July 2022 / Accepted: 20 July 2022 / Published: 22 July 2022
(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials)
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Abstract

The main aim of this study is to define degenerate Genocchi polynomials and numbers of the second kind by using logarithmic functions, and to investigate some of their analytical properties and some applications. For this purpose, many formulas and relations for these polynomials, including some implicit summation formulas, differentiation rules and correlations with the earlier polynomials by utilizing some series manipulation methods, are derived. Additionally, as an application, the zero values of degenerate Genocchi polynomials and numbers of the second kind are presented in tables and multifarious graphical representations for these zero values are shown.
Keywords: degenerate Genocchi polynomials; degenerate Genocchi polynomials of the second kind; summation formulae; Stirling numbers degenerate Genocchi polynomials; degenerate Genocchi polynomials of the second kind; summation formulae; Stirling numbers

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MDPI and ACS Style

Khan, W.A.; Alatawi, M.S. Analytical Properties of Degenerate Genocchi Polynomials of the Second Kind and Some of Their Applications. Symmetry 2022, 14, 1500. https://doi.org/10.3390/sym14081500

AMA Style

Khan WA, Alatawi MS. Analytical Properties of Degenerate Genocchi Polynomials of the Second Kind and Some of Their Applications. Symmetry. 2022; 14(8):1500. https://doi.org/10.3390/sym14081500

Chicago/Turabian Style

Khan, Waseem Ahmad, and Maryam Salem Alatawi. 2022. "Analytical Properties of Degenerate Genocchi Polynomials of the Second Kind and Some of Their Applications" Symmetry 14, no. 8: 1500. https://doi.org/10.3390/sym14081500

APA Style

Khan, W. A., & Alatawi, M. S. (2022). Analytical Properties of Degenerate Genocchi Polynomials of the Second Kind and Some of Their Applications. Symmetry, 14(8), 1500. https://doi.org/10.3390/sym14081500

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