Advances in the generalized Cesàro polynomials
Cesàro polynomials have been extended in various ways and applied in diverse areas. In this paper, we aim to introduce a multivariable and multiparameter generalization of Cesàro polynomials. Then we explore several generating functions, an addition formula, a differential-recurrence relation, a mu...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2024-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/644 |
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| _version_ | 1850058222309736448 |
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| author | N. Özmen E. Erkuş-Duman |
| author_facet | N. Özmen E. Erkuş-Duman |
| author_sort | N. Özmen |
| collection | DOAJ |
| description |
Cesàro polynomials have been extended in various ways and applied in diverse areas. In this paper, we aim to introduce a multivariable and multiparameter generalization of Cesàro polynomials. Then we explore several generating functions, an addition formula, a differential-recurrence relation, a multiple integral formula for this extended Cesàro polynomial, as well as a multiple integral formula whose kernel is this extended Cesàro polynomial. Also we present several bilinear and bilateral generating functions for this extended Ces`aro polynomial, two of whose examples are demonstrated.
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| format | Article |
| id | doaj-art-af4bb91df6e845ba97643f0daaf7e760 |
| institution | DOAJ |
| issn | 2518-7929 2663-5011 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj-art-af4bb91df6e845ba97643f0daaf7e7602025-08-20T02:51:14ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112024-12-01116410.31489/2024m4/159-169Advances in the generalized Cesàro polynomialsN. Özmen0https://orcid.org/0000-0001-7555-1964E. Erkuş-Duman 1https://orcid.org/0000-0003-1848-5248D¨uzce University, D¨uzce, T¨urkiyeGazi University, Ankara, T¨urkiye Cesàro polynomials have been extended in various ways and applied in diverse areas. In this paper, we aim to introduce a multivariable and multiparameter generalization of Cesàro polynomials. Then we explore several generating functions, an addition formula, a differential-recurrence relation, a multiple integral formula for this extended Cesàro polynomial, as well as a multiple integral formula whose kernel is this extended Cesàro polynomial. Also we present several bilinear and bilateral generating functions for this extended Ces`aro polynomial, two of whose examples are demonstrated. https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/644Cesàro polynomialsgenerating functionrecurrence relationhypergeometric functionintegral representation |
| spellingShingle | N. Özmen E. Erkuş-Duman Advances in the generalized Cesàro polynomials Қарағанды университетінің хабаршысы. Математика сериясы Cesàro polynomials generating function recurrence relation hypergeometric function integral representation |
| title | Advances in the generalized Cesàro polynomials |
| title_full | Advances in the generalized Cesàro polynomials |
| title_fullStr | Advances in the generalized Cesàro polynomials |
| title_full_unstemmed | Advances in the generalized Cesàro polynomials |
| title_short | Advances in the generalized Cesàro polynomials |
| title_sort | advances in the generalized cesaro polynomials |
| topic | Cesàro polynomials generating function recurrence relation hypergeometric function integral representation |
| url | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/644 |
| work_keys_str_mv | AT nozmen advancesinthegeneralizedcesaropolynomials AT eerkusduman advancesinthegeneralizedcesaropolynomials |