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

Khan, Waseem A.; Alatawi, Maryam Salem

doi:10.3390/sym14081500

Cited by 5 publications

(2 citation statements)

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“…Very recently, a large interest has been shown by mathematicians to introduce ∆ h forms of special polynomials. Some extensions of the special polynomials were studied in [1,[5][6][7][8][9][10]. After that, by using the classical finite difference operator ∆ h , a new form of the special polynomials, known as the ∆ h special polynomials of different polynomials, were introduced in [11,12].…”

Section: Introductionmentioning

confidence: 99%

Investigating the Properties and Dynamic Applications of Δh Legendre–Appell Polynomials

Alam,

Wani,

Khan

et al. 2024

Mathematics

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This research aims to introduce and examine a new type of polynomial called the Δh Legendre–Appell polynomials. We use the monomiality principle and operational rules to define the Δh Legendre–Appell polynomials and explore their properties. We derive the generating function and recurrence relations for these polynomials and their explicit formulas, recurrence relations, and summation formulas. We also verify the monomiality principle for these polynomials and express them in determinant form. Additionally, we establish similar results for the Δh Legendre–Bernoulli, Euler, and Genocchi polynomials.

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Section: Introductionmentioning

confidence: 99%

Investigating the Properties and Dynamic Applications of Δh Legendre–Appell Polynomials

Alam,

Wani,

Khan

et al. 2024

Mathematics

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“…Many researchers [1][2][3][4][5] defined and constructed generating maps for novel families of special polynomials, such as Bernoulli, Euler, and Genocchi by utilizing Changhee and Changhee-Genocchi polynomials. These studies provided fundamental properties and diverse applications for these polynomials.…”

Section: Introductionmentioning

confidence: 99%

A Note on Modified Degenerate Changhee–Genocchi Polynomials of the Second Kind

Khan

Alatawi

2023

Symmetry

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In this study, we introduce modified degenerate Changhee–Genocchi polynomials of the second kind, and analyze some properties by providing several relations and applications. We first attain diverse relations and formulas covering addition formulas, recurrence rules, implicit summation formulas, and relations with the earlier polynomials in the literature. By using their generating function, we derive some new relations, including the Stirling numbers of the first and second kinds. Moreover, we introduce modified higher-order degenerate Changhee–Genocchi polynomials of the second kind. We also derive some new identities and properties of this type of polynomials.

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