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

Authors : GÖKSAL BİLGİCİ, ÜMİT TOKAŞER, ZAFER ÜNAL

Pages : 102-113

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Publication Date : 2017-10-15

Article Type : Research Paper

Abstract :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