Dual-hyperbolic Fibonacci and Lucas numbers with Fibonacci and Lucas coefficients are introduced by Cihan et al. and some identities and theorems are given regarding modules and conjugates of these numbers. Later, generating function and Binet's formula with the help of this generating function have been derived. Also, Binet formula, Cassini's, Catalan's, d'Ocagne's, Honsberger and Tagiuri identities are found for dual-hyperbolic numbers with generalized Fibonacci and Lucas coefficients. While these operations are being done, we will benefit from the well-known Fibonacci and Lucas identities. Moreover, it is seen that the results which are obtained for the values $p = 1$ and $q = 0$ corresponds to the theorems in the article by Cihan et al. [1].
Dual-hyperbolic numbers Generalized Fibonacci numbers Generalized Lucas numbers
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 20 Aralık 2019 |
Gönderilme Tarihi | 9 Eylül 2019 |
Kabul Tarihi | 24 Ekim 2019 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 2 |