On Generalized Quaternions Whose Components are Higher-Order Generalized Fibonacci Hyper-Numbers With q$$ q $$-Integer Numbers
Emrah Polatli
article (Uluslararası, Hakemli) | Yazar(lar): Emrah Polatli | Yıl: 2026 | Dergi/Kurum: MATHEMATICAL METHODS IN THE APPLIED SCIENCES | İndeks: WOS.SCI | DOI: 10.1002/mma.70596 | Anahtar Kelimeler: Binet-like formula, generalized quaternions, higher-order Fibonacci numbers, hyper-numbers, q$$ q $$-integers — Özet: The ma
The main aim of this paper is to introduce generalized quaternions whose components are higher-order generalized Fibonacci hyper-numbers with -integer numbers. We first derive the Binet-like formula for this newly established type of generalized quaternions. With the help of the Binet-like formula, we give recurrence relation, generating function, exponential generating function, and some useful summation properties of these generalized quaternions.