A study on hyperbolic numbers with generalized Jacobsthal numbers components
Yueksel Soykan, Erkan Tasdemir
article (Uluslararası, Hakemli) | Yazar(lar): Yueksel Soykan, Erkan Tasdemir | Yıl: 2022 | Dergi/Kurum: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS | İndeks: WOS.ESCI | DOI: 10.22075/ijnaa.2021.22113.2328 | Anahtar Kelimeler: Jacobsthal numbers, Jacobsthal-Lucas numbers, hyperbolic numbers, hyperbolic
In this paper, we introduce the generalized hyperbolic Jacobsthal numbers. As special cases, we deal with hyperbolic Jacobsthal and hyperbolic Jacobsthal-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 with these sequences.