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Relevant bibliographies by topics / Generalized Multi poly-Euler polynomials

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Academic literature on the topic 'Generalized Multi poly-Euler polynomials'

Author: Grafiati

Published: 3 June 2025

Last updated: 22 June 2025

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Journal articles on the topic "Generalized Multi poly-Euler polynomials"

1

Corcino, Roberto B., Hassan Jolany, Cristina B. Corcino, and Takao Komatsu. "On Generalized Multi Poly-Euler Polynomials." Fibonacci Quarterly 55, no. 1 (2017): 41–53. http://dx.doi.org/10.1080/00150517.2017.12427790.

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2

Kim, Taekyun, Dae San Kim, Jin-Woo Park, and Jongkyum Kwon. "A Note on Multi-Euler–Genocchi and Degenerate Multi-Euler–Genocchi Polynomials." Journal of Mathematics 2023 (August 26, 2023): 1–7. http://dx.doi.org/10.1155/2023/3810046.

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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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3

El-Desouky, Beih, Rabab Gomaa, and Alia Magar. "The multi-variable unified family of generalized Apostol-type polynomials." Applicable Analysis and Discrete Mathematics, no. 00 (2020): 15. http://dx.doi.org/10.2298/aadm190405015e.

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The aim of this paper is to investigate and give a new family of multi-variable Apostol-type polynomials. This family is related to Apostol-Euler, Apostol-Bernoulli, Apostol-Genocchi and Apostol-laguerre polynomials. Moreover, we derive some implicit summation formulae and general symmetry identities. The new family of polynomials introduced here, gives many interesting special cases.

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4

Sweilam, N. H., S. M. AL-Mekhlafi, and D. Baleanu. "Efficient numerical treatments for a fractional optimal control nonlinear Tuberculosis model." International Journal of Biomathematics 11, no. 08 (2018): 1850115. http://dx.doi.org/10.1142/s1793524518501152.

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In this paper, the general nonlinear multi-strain Tuberculosis model is controlled using the merits of Jacobi spectral collocation method. In order to have a variety of accurate results to simulate the reality, a fractional order model of multi-strain Tuberculosis with its control is introduced, where the derivatives are adopted from Caputo’s definition. The shifted Jacobi polynomials are used to approximate the optimality system. Subsequently, Newton’s iterative method will be used to solve the resultant nonlinear algebraic equations. A comparative study of the values of the objective functional, between both the generalized Euler method and the proposed technique is presented. We can claim that the proposed technique reveals better results when compared to the generalized Euler method.

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5

Araci, Serkan, Mumtaz Riyasat, Shahid Wani, and Subuhi Khan. "A New Class of Hermite-Apostol Type Frobenius-Euler Polynomials and Its Applications." Symmetry 10, no. 11 (2018): 652. http://dx.doi.org/10.3390/sym10110652.

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The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several explicit relations involving Hurwitz–Lerch Zeta functions and some summation formulae related to these polynomials are derived. Further, we establish certain symmetry identities involving generalized power sums and Hurwitz–Lerch Zeta functions. An operational view for these polynomials is presented, and corresponding applications are given. The illustrative special cases are also mentioned along with their generating equations.

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Bilgic, Secil, and Veli Kurt. "On generalized q-poly-Bernoulli numbers and polynomials." Filomat 34, no. 2 (2020): 515–20. http://dx.doi.org/10.2298/fil2002515b.

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Many mathematicians in ([1],[2],[5],[14],[20]) introduced and investigated the generalized q-Bernoulli numbers and polynomials and the generalized q-Euler numbers and polynomials and the generalized q-Gennochi numbers and polynomials. Mahmudov ([15],[16]) considered and investigated the q-Bernoulli polynomials B(?)n,q(x,y) in x,y of order ? and the q-Euler polynomials E(?) n,q (x,y)in x,y of order ?. In this work, we define generalized q-poly-Bernoulli polynomials B[k,?] n,q (x,y) in x,y of order ?. We give new relations between the generalized q-poly-Bernoulli polynomials B[k,?] n,q (x,y) in x,y of order ? and the generalized q-poly-Euler polynomials ?[k,?] n,q (x,y) in x,y of order ? and the q-Stirling numbers of the second kind S2,q(n,k).

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7

Kurt, Veli. "On the generalized q-poly-Euler polynomials of the second kind." Filomat 34, no. 2 (2020): 475–82. http://dx.doi.org/10.2298/fil2002475k.

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In this work, we define the generalized q-poly-Euler numbers of the second kind of order ? and the generalized q-poly-Euler polynomials of the second kind of order ?. We investigate some basic properties for these polynomials and numbers. In addition, we obtain many identities, relations including the Roger-Sz?go polynomials, the Al-Salam Carlitz polynomials, q-analogue Stirling numbers of the second kind and two variable Bernoulli polynomials.

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8

Khan, Waseem Ahmad, Mehmet Acikgoz, and Ugur Duran. "Note on the Type 2 Degenerate Multi-Poly-Euler Polynomials." Symmetry 12, no. 10 (2020): 1691. http://dx.doi.org/10.3390/sym12101691.

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Kim and Kim (Russ. J. Math. Phys. 26, 2019, 40-49) introduced polyexponential function as an inverse to the polylogarithm function and by this, constructed a new type poly-Bernoulli polynomials. Recently, by using the polyexponential function, a number of generalizations of some polynomials and numbers have been presented and investigated. Motivated by these researches, in this paper, multi-poly-Euler polynomials are considered utilizing the degenerate multiple polyexponential functions and then, their properties and relations are investigated and studied. That the type 2 degenerate multi-poly-Euler polynomials equal a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind is proved. Moreover, an addition formula and a derivative formula are derived. Furthermore, in a special case, a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers is shown.

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9

Jolany, Hassan, Roberto B. Corcino, and Takao Komatsu. "More properties on multi-poly-Euler polynomials." Boletín de la Sociedad Matemática Mexicana 21, no. 2 (2015): 149–62. http://dx.doi.org/10.1007/s40590-015-0061-y.

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10

Corcino, Roberto, Cristina Corcino, and Waseem Khan. "On Type 2 Degenerate Poly-Frobenius-Euler Polynomials." Recoletos Multidisciplinary Research Journal 13, no. 1 (2025): 13–31. https://doi.org/10.32871/rmrj2513.01.02.

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Background: This paper introduces a class of special polynomials called Type 2 degenerate poly-Frobenius-Euler polynomials, defined using the polyexponential function. Motivated by the expanding theory of degenerate versions of classical polynomials, the paper seeks to enrich the mathematical landscape by constructing generalized structures with deeper combinatorial and analytic properties. Methods: The study employs the method of generating functions combined with Cauchy's rule for the product of two series to derive explicit formulas and identities, enabling systematic manipulation of series expansions. From an analytic perspective, the authors utilized the comparison test and principles of uniform convergence to establish that certain integral representations correspond to holomorphic functions. Results: The researchers successfully derived explicit formulas and identities for the Type 2 degenerate poly-Frobenius-Euler polynomials. They established meaningful connections with the degenerate Stirling numbers of the first and second kinds. Furthermore, they introduced the Type 2 degenerate unipoly-poly-Frobenius-Euler polynomials, defined via the unipoly function, and thoroughly investigated their various properties, including behaviors under differentiation and integration. Conclusion: The study significantly advances the theory of degenerate polynomials by constructing new polynomial families, derivation of explicit identities, and establishing analytic properties. It opens new avenues for future research by bridging classical and generalized combinatorial sequences within a robust analytic framework.

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Book chapters on the topic "Generalized Multi poly-Euler polynomials"

1

Corcino, Roberto B. "Multi Poly-Bernoulli and Multi Poly-Euler Polynomials." In Applied Mathematical Analysis: Theory, Methods, and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-99918-0_21.

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