p-Bernoulli and geometric polynomials

In the present paper, we deﬁne the generalized Kwang-Wu Chen matrix. Basic properties of this generalization, such as explicit formulas and generating functions are presented. Moreover, we focus on a new class of generalized Fubini polynomials. Then we discuss their relationship with other polynomials such as Fubini, Bell, Eulerian and Frobenius-Euler polynomials. We have also investigated some basic properties related to the degenerate generalized Fubini polynomials.

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“…we apply (4.9), we get The Fubini polynomials of two variables ω n (x, y) are defined in [8,9,11] by the following generating function…”

Section: On Generalized Fubini Polynomialsmentioning

confidence: 99%

Generalized Fubini transform with two variables

Sebaoui

Laissaoui

Guettai

et al. 2023

Hacettepe Journal of Mathematics and Statistics

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“…Replacing x by x y λ in (4.9) and multiplying both sides by y n e −λ and integrating for λ from zero to infinity, and by comparing with (4.2) we get (4.10). Now to prove (4.11), using (4.10), we have The Fubini polynomials of two variables ω n (x, y) are defined in [7,8,10] by the following generating function…”

Section: On Generalized Fubini Polynomialsmentioning

confidence: 99%

Generalized Fubini transform with two variables

Sebaoui¹,

Laissaoui²,

Guettai³

et al. 2022

Preprint

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This paper aims to investigate a new class of generalized Fubini polynomials. Firstly, we derive a general identity which generalizes the Fubini transform of a sequence. Secondly, we give in particular case and we establish a relationship between generalized Fubini polynomials and more polynomials as Fubini, Bell, Eulerian and Frobenius-Euler polynomials. Finally, we give the probabilistic representation and the degenerate of this class.

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“…Geometric polynomials arise from the following generating function and some of its generalisations 1 2−e x . The polynomials are well known in the literature, for instance in [2,9,10,15,16,27,29]. One generalisation of geometric polynomials is higher order generalized geometric polynomials which seem to first appear in [17], and their generating function is…”

Section: Introductionmentioning

confidence: 99%

A second type of higher order generalized geometric polynomials and higher order generalized Euler polynomials

Corcino

Çekіm

et al. 2020

Quaestiones Mathematicae

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In this study we introduce a second type of higher order generalized geometric polynomials. This we achieve by examining the generalized stirling numbers S (n, k, α, β, γ) [Hsu and Shiue, 1998] for some negative arguments. We study their number theoretic properties, asymptotic properties, and their combinatorial properties using the notion of barred preferential arrangements. We also proposed a generalisation of the classical Euler polynomials and show how these generalized Euler polynomials are related to the second type of higher order generalized geometric polynomials.

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p-Bernoulli and geometric polynomials

Cited by 9 publications

References 22 publications

Generalized Fubini transform with two variables

Generalized Fubini transform with two variables

Generalized Fubini transform with two variables

A second type of higher order generalized geometric polynomials and higher order generalized Euler polynomials

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