Unification of Two-Variable Family of Apostol-Type Polynomials with Applications

In this paper, the two-variable unified family of generalized Apostol-type polynomials is introduced, and some implicit forms and general symmetry identities are derived. Also, we obtain new degenerate Apostol-type numbers and polynomials constructed from the new 2-variable unified family. We derive...

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Main Authors: Beih S. El-Desouky, Rabab S. Gomaa, Alia M. Magar
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/4514725
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author Beih S. El-Desouky
Rabab S. Gomaa
Alia M. Magar
author_facet Beih S. El-Desouky
Rabab S. Gomaa
Alia M. Magar
author_sort Beih S. El-Desouky
collection DOAJ
description In this paper, the two-variable unified family of generalized Apostol-type polynomials is introduced, and some implicit forms and general symmetry identities are derived. Also, we obtain new degenerate Apostol-type numbers and polynomials constructed from the new 2-variable unified family. We derive explicit formulae of polynomials and identities that include some special numbers and polynomials. In addition, a probabilistic representation of the new family and some statistical properties are obtained.
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institution Kabale University
issn 2314-4785
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publishDate 2022-01-01
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series Journal of Mathematics
spelling doaj-art-02e2e0d7cbac43e3a19ac68f7cc540fd2025-02-03T01:06:34ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4514725Unification of Two-Variable Family of Apostol-Type Polynomials with ApplicationsBeih S. El-Desouky0Rabab S. Gomaa1Alia M. Magar2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn this paper, the two-variable unified family of generalized Apostol-type polynomials is introduced, and some implicit forms and general symmetry identities are derived. Also, we obtain new degenerate Apostol-type numbers and polynomials constructed from the new 2-variable unified family. We derive explicit formulae of polynomials and identities that include some special numbers and polynomials. In addition, a probabilistic representation of the new family and some statistical properties are obtained.http://dx.doi.org/10.1155/2022/4514725
spellingShingle Beih S. El-Desouky
Rabab S. Gomaa
Alia M. Magar
Unification of Two-Variable Family of Apostol-Type Polynomials with Applications
Journal of Mathematics
title Unification of Two-Variable Family of Apostol-Type Polynomials with Applications
title_full Unification of Two-Variable Family of Apostol-Type Polynomials with Applications
title_fullStr Unification of Two-Variable Family of Apostol-Type Polynomials with Applications
title_full_unstemmed Unification of Two-Variable Family of Apostol-Type Polynomials with Applications
title_short Unification of Two-Variable Family of Apostol-Type Polynomials with Applications
title_sort unification of two variable family of apostol type polynomials with applications
url http://dx.doi.org/10.1155/2022/4514725
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AT rababsgomaa unificationoftwovariablefamilyofapostoltypepolynomialswithapplications
AT aliammagar unificationoftwovariablefamilyofapostoltypepolynomialswithapplications