A note on hyperbolic (p,q)-Fibonacci quaternions

Year 2020, Volume: 69 Issue: 1, 880 - 890, 30.06.2020

Tülay Yağmur

https://doi.org/10.31801/cfsuasmas.582674

Cited By: 2

Abstract

In this paper, we introduce a new quaternion sequence called  hyperbolic (p,q)-Fibonacci  quaternions.  This new quaternion sequence includes hyperbolic Fibonacci, hyperbolic k-Fibonacci, hyperbolic  Pell, hyperbolic k-Pell, hyperbolic  Jacobsthal, hyperbolic k-Jacobsthal quaternions. We give generating function and Binet formula for these quaternions. We also obtain   some  identities such as d'Ocagne's, Catalan's and Cassini's identities involving  hyperbolic (p,q)-Fibonacci  quaternions.

Keywords

Fibonacci numbers, (p;q)-Fibonacci numbers, (p;q)-Fibonacci quaternions, hyperbolic quaternions, hyperbolic (p;q)-Fibonacci quaternions

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