POLYNOMIALS OF BALANCING, BALANCING-LUCAS SEQUENCES AND k-BALANCING, k-BALANCING-LUCAS SEQUENCES

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Özkan E., Eser E., Uysal M.

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, cilt.47, sa.1, ss.97-109, 2026 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 47 Sayı: 1
• Basım Tarihi: 2026
• Doi Numarası: 10.22190/fumi240529009o
• Dergi Adı: FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
• Sayfa Sayıları: ss.97-109
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

In this work, we introduce Balancing, Balancing-Lucas polynomials, and k−Balancing, k−Balancing-Lucas polynomials. We exhibit some important theorems: Cassini, Catalan, Vajda, d’Ocagne, and Honsberger identities for Balancing, BalancingLucas polynomials, and k−Balancing, k−Balancing-Lucas polynomials. We give the concepts of recurrence relation, characteristic equation, roots of the characteristic equation, Binet formula, and generating function for polynomials, which are important for number sequences.