p-Analogue of biperiodic Pell and Pell–Lucas polynomials

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Kuloğlu B., Özkan E., Shannon A. G.

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, cilt.29, sa.2, ss.336-347, 2023 (ESCI, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 29 Sayı: 2
• Basım Tarihi: 2023
• Doi Numarası: 10.7546/nntdm.2023.29.2.336-347
• Dergi Adı: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
• Sayfa Sayıları: ss.336-347
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Marmara Üniversitesi Adresli: Hayır

Özet

In this study, a binomial sum, unlike but analogous to the usual binomial sums, is expressed with a different definition and termed the p-integer sum. Based on this definition, p-analogue Pell and Pell–Lucas polynomials are established and the generating functions of these new polynomials are obtained. Some theorems and propositions depending on the generating functions are also expressed. Then, by association with these, the polynomials of so-called ‘incomplete’ number sequences have been obtained, and elegant summation relations provided. The paper has also been placed in the appropriate historical context for ease of further development.