GÖKSAL BİLGİCİ, ÜMİT TOKAŞER, ZAFER ÜNAL

$k$-FIBONACCI AND $k$-LUCAS GENERALIZED QUATERNIONS

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.

Keywords:

$k$-Fibonacci number, $k$-Lucas number, generalized quaternion,

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Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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