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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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| 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. |
| format | Article |
| id | doaj-art-02e2e0d7cbac43e3a19ac68f7cc540fd |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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