POLYNOMIALS OF BALANCING, BALANCING-LUCAS SEQUENCES AND k-BALANCING, k-BALANCING-LUCAS SEQUENCES
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, vol.47, no.1, pp.97-109, 2026 (ESCI)
- Publication Type: Article / Article
- Volume: 47 Issue: 1
- Publication Date: 2026
- Doi Number: 10.22190/fumi240529009o
- Journal Name: FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
- Journal Indexes: Emerging Sources Citation Index (ESCI)
- Page Numbers: pp.97-109
- Open Archive Collection: AVESIS Open Access Collection
- Erzincan Binali Yildirim University Affiliated: Yes
Abstract
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.