Exploring the depths of degenerate hyper-harmonic numbers in view of harmonic functions

Volume 35, Issue 2, pp 136--148 https://dx.doi.org/10.22436/jmcs.035.02.02

Publication Date: April 19, 2024 Submission Date: December 05, 2023 Revision Date: December 20, 2023 Accteptance Date: January 15, 2024

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Authors

A. Al e'damat - Department of Mathematics, Faculty of Science, Al-Hussein Bin Talal University, P.O. Box 20, Maan, Jordan. W. A. Khan - Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia. U. Duran - Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, Hatay 31200, Turkiye. S. A. K. Kirmani - Department of Electrical Engineering, College of Engineering, Qassim University, Unaizah, Saudi Arabia. Ch.-S. Ryoo - Department of Mathematics, Hannam University, Daejeon 34430, South Korea.

Abstract

This study aims to analyze several properties and relations of the degenerate hyper-harmonic numbers and the degenerate harmonic numbers. For this purpose, many identities including the Daehee numbers and derangement numbers, and degenerate Stirling numbers of the first kind are provided. Moreover, the first few values of the degenerate hyper-harmonic numbers are given and some graphical representations are shown.

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Keywords

• Hyper-harmonic numbers
• degenerate hyper-harmonic numbers
• degenerate Daehee numbers
• differential equation

MSC

•  05A19
•  11B37
•  34A30

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