Some Identities of the Degenerate Multi-Poly-Bernoulli Polynomials of Complex Variable

Muhiuddin, G.; Khan, Waseem A.; Duran, Ugur; Al-Kadi, Deena

doi:10.1155/2021/7172054

Cited by 12 publications

(5 citation statements)

References 23 publications

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“…The Apostol-type Bernoulli polynomials B (α) j (ξ; λ) of order α, the Apostol-type Euler polynomials E (α) j (ξ; λ) of order α and the Apostol-type Genocchi polynomials G (α) j (ξ; λ) of order α are defined by (see [10,16,24,26]):…”

Section: Introductionmentioning

confidence: 99%

Certain properties on Bell-based Apostol-type Frobenius-Genocchi polynomials of complex variable

Al edamat,

Khan,

Ryoo

2024

J. Math. Computer Sci.

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In this study, we introduce sine and cosine Bell-based Frobenius-type Genocchi polynomials, and by presenting several relations and applications, we analyze certain properties. Our first step is to obtain diverse relations and formulas that cover summation formulas, addition formulas, relations with earlier polynomials in the literature, and differentiation rules. Finally, after determining the first few zero values of the Frobenius-type Genocchi polynomials, we draw graphical representations of these zero values.

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Section: Introductionmentioning

confidence: 99%

Certain properties on Bell-based Apostol-type Frobenius-Genocchi polynomials of complex variable

Al edamat,

Khan,

Ryoo

2024

J. Math. Computer Sci.

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“…Some of the most significant polynomials in the theory of special polynomials are the Bell, Euler, Bernoulli, Hermite, and Genocchi polynomials. Recently, the aforesaid polynomials and their diverse generalizations have been densely considered and investigated by many physicists and mathematicians (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]22]) and see also the references cited therein (see [6][7][8][9][14][15][16][17]). The class of Appell polynomial sequence is one of the significant classes of polynomials sequence [1].…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the importance and potential applications in certain problems in number theory, combinatorics, classical and numerical analysis and physics, several families of Bernoulli and Euler polynomials and special polynomials have been recently studied by many authors, see [8,9,[19][20][21]. Recently, Kim et al [13,16] have introduced the degenerate Bernoulli and degenerate Euler polynomials of a complex variable.…”

Section: Introductionmentioning

confidence: 99%

A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable

Alam¹,

Khan²,

Obeidat³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In this article, we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler polynomials. Some fundamental properties of these functions are given. By using these generating functions and some identities, relations among trigonometric functions and two parametric kinds of Bell-based Bernoulli and Euler polynomials, Stirling numbers are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are given.

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“…The classical Genocchi numbers G n , the classical Genocchi polynomials G n (x) and the generalized Genocchi polynomials G (α) n (x) of (real or complex) order α are usually defined by means of the following generating functions (see [11,12,[15][16][17][18][19][20][21][22][23][24]):…”

Section: Introductionmentioning

confidence: 99%