Advances in the generalized Cesàro polynomials

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Özmen N., Erkuş-Duman E.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, cilt.116, sa.4, ss.159-169, 2024 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 116 Sayı: 4
• Basım Tarihi: 2024
• Doi Numarası: 10.31489/2024m4/159-169
• Dergi Adı: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
• Sayfa Sayıları: ss.159-169
• Gazi Üniversitesi Adresli: Evet

Özet

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.