Properties of hyperbolic generalized Pell numbers
Yueksel Soykan, Melih Gocen
article (Uluslararası, Hakemli) | Yazar(lar): Yueksel Soykan, Melih Gocen | Yıl: 2020 | Dergi/Kurum: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | İndeks: WOS.ESCI | DOI: 10.7546/nntdm.2020.26.4.136-153 | Anahtar Kelimeler: Pell numbers, Pell-Lucas numbers, Hyperbolic numbers, Hyperbolic Pell numbers, Cassini ident
In this paper, we introduce the generalized hyperbolic Pell numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Pell and hyperbolic Pell-Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesaro's, Melham's identities and present matrices related to these sequences.