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

Year 2017, Volume: 5 Issue: 2, 102 - 113, 15.10.2017

GÖKSAL Bilgici ÜMİT Tokaşer ZAFER Ünal

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

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