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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2023.03.006

Degenerate Harmonic Numbers and Polynomials with Combinatorial Sequences

Rui Wang, Wuyungaowa*

Department of Mathematics, College of Sciences and Technology, Inner Mongolia University, Huhhot, Inner Mongolia, China.

*Corresponding author: Wuyungaowa

Published: April 12,2023

Abstract

Since the harmonic numbers were introduced, various types of harmonic numbers have been presented. In 2004, T. Kim and D. Kim first introduce the degenerate harmonic numbers and polynomials, moreover, those numbers and polynomials have been studied by many authors. In this paper, by using the Riordan arrays and generating functions, we derive a series of new combinatorial identities with respect to the degenerate harmonic numbers and polynomials. In first, we introduce the concept of the degenerate harmonic numbers, and obtain some properties and equalities of these numbers in terms of generating functions and Riordan arrays. Then we introduce the degenerate harmonic polynomials. Applying generating functions methods, we discuss some character involving the degenerate harmonic polynomials. Finally, we establish some new identities involving the degenerate harmonic polynomials with other special combinatorial numbers as well as polynomials, such as the degenerate Bernoulli numbers, the degenerate Euler numbers, and the various degenerate Daehee numbers and so on.

Keywords

The degenerate harmonic numbers and polynomials, Generating function, Various degenerate Daehee numbers, The Bell numbers, Two kinds of degenerate stirling numbers

References

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How to cite this paper

Degenerate Harmonic Numbers and Polynomials with Combinatorial Sequences

How to cite this paper:  Rui Wang, Wuyungaowa. (2023) Degenerate Harmonic Numbers and Polynomials with Combinatorial SequencesJournal of Applied Mathematics and Computation7(1), 53-64.

DOI: http://dx.doi.org/10.26855/jamc.2023.03.006