On generalized degenerate Euler–Genocchi polynomials

Kim, Taekyun; Ким, Дае Сан; Kim, Hye Kyung

doi:10.1080/27690911.2022.2159958

Cited by 14 publications

(12 citation statements)

References 11 publications

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“…Carlitz [21,22] initiated the theory of degenerate polynomials by introducing the degenerate forms of the conventional Bernoulli and Euler polynomials. Later, mathematicians investigated degenerate versions of several special numbers and polynomials, such as degenerate Stirling numbers and polynomials [23,24], degenerate Bernoulli and Euler polynomials [25], degenerate generalized Bell polynomials [26], degenerate generalized Laguerre polynomials [27], degenerate Gould-Hopper polynomials [28], degenerate Hermite polynomials [29], and so on (see [30][31][32] and the references therein). It is also worth mentioning that the study of degenerate versions of polynomials and numbers extends to special functions, such as the Euler zeta function [33], the gamma, digamma, and polygamma functions [34,35], and degenerate hypergeometric functions [36,37].…”

Section: Some Definitions Related To the Concept Of Degeneratementioning

confidence: 99%

Novel Kinds of Fractional λ–Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral

Alqarni,

Abdalla

2023

Mathematics

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In recent years, fractional kinetic equations (FKEs) involving various special functions have been widely used to describe and solve significant problems in control theory, biology, physics, image processing, engineering, astrophysics, and many others. This current work proposes a new solution to fractional λ−kinetic equations based on generalized degenerate hypergeometric functions (GDHFs), which has the potential to be applied to calculate changes in the chemical composition of stars such as the sun. Furthermore, this expanded form can also help to solve various problems with phenomena in physics, such as fractional statistical mechanics, anomalous diffusion, and fractional quantum mechanics. Moreover, some of the well-known outcomes are just special cases of this class of pathway-type solutions involving GDHFs, with greater accuracy, while providing an easily calculable solution. Additionally, numerical graphs of these analytical solutions, using MATLAB Software (latest version 2023b), are also considered.

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Section: Some Definitions Related To the Concept Of Degeneratementioning

confidence: 99%

Novel Kinds of Fractional λ–Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral

Alqarni,

Abdalla

2023

Mathematics

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“…Goubi introduced the generalized Euler-Genocchi polynomials (of order α) in [5]. A degenerate version of those polynomials, namely the generalized degenerate Euler-Genocchi polynomials, is investigated in [10]. Here we study a'multi-version' of them, namely the multi-Euler-Genocchi and degenerate multi-Euler-Genocchi polynomials.…”

Section: Introductionmentioning

confidence: 99%

A note on multi-Euler-Genocchi and degenerate multi-Euler-Genocchi polynomials

Kim¹,

Ким²,

park³

et al. 2023

Preprint

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Recently, introduced are the generalized Euler-Genocchi and generalized degenerate Euler-Genocchi polynomials. The aim of this note is to study the multi-Euler-Genocchi and degenerate multi-Euler-Genocchi polynomials which are defined by means of the multiple logarithm and generalize respectively the generalized Euler-Genocchi and generalized degenerate Euler-Genocchi polynomials. Especially, we express the former by the generalized Euler-Genocchi polynomials, the multi-Stirling numbers of the first kind and Stirling numbers of the second kind, and the latter by the generalized degenerate Euler-Genocchi polynomials, the multi-Stirling numbers of the first kind and Stirling numbers of the second kind.

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“…Note that lim λ ⟶ 0 E n,λ (x) � E n (x), (n ≥ 0). In view of (2), the degenerate Genocchi polynomials are defned by the following (see [19,20]):…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the generalized degenerate Euler-Genocchi polynomials are defned by the following (see [20]):…”

Section: Introductionmentioning

confidence: 99%

A Note on Multi-Euler–Genocchi and Degenerate Multi-Euler–Genocchi Polynomials

Kim,

Park

et al. 2023

Journal of Mathematics

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Recently, the generalized Euler–Genocchi and generalized degenerate Euler–Genocchi polynomials are introduced. The aim of this note is to study the multi-Euler–Genocchi and degenerate multi-Euler–Genocchi polynomials which are defined by means of the multiple logarithm and generalize, respectively, the generalized Euler–Genocchi and generalized degenerate Euler–Genocchi polynomials. Especially, we express the former by the generalized Euler–Genocchi polynomials, the multi-Stirling numbers of the first kind and Stirling numbers of the second kind, and the latter by the generalized degenerate Euler–Genocchi polynomials, the multi-Stirling numbers of the first kind and Stirling numbers of the second kind.

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On generalized degenerate Euler–Genocchi polynomials

Cited by 14 publications

References 11 publications

Novel Kinds of Fractional λ–Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral

Novel Kinds of Fractional λ–Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral

A note on multi-Euler-Genocchi and degenerate multi-Euler-Genocchi polynomials

A Note on Multi-Euler–Genocchi and Degenerate Multi-Euler–Genocchi Polynomials

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