We investigate the properties of $k-$Fibonacci and $k-$Lucas quaternions over the generalized quaternion algebra. After presenting generating functions and Binet's formulas for these types of quaternions, we calculate several well-known identities such as Catalan's, Cassini's and d'Ocagne's identities for $k-$Fibonacci and $k-$Lucas generalized quaternions.
$k$-Fibonacci number $k$-Lucas number generalized quaternion
Konular | Mühendislik |
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Bölüm | Articles |
Yazarlar | |
Yayımlanma Tarihi | 15 Ekim 2017 |
Gönderilme Tarihi | 15 Ekim 2017 |
Kabul Tarihi | 7 Haziran 2017 |
Yayımlandığı Sayı | Yıl 2017 Cilt: 5 Sayı: 2 |