Some summation identities for fibonacci quaternions and hyper-fibonacci quaternions∗

F. A.M.A. Aldhuhouri; M. M. Al Obeidli; H. H. Leung

Some summation identities for fibonacci quaternions and hyper-fibonacci quaternions^∗

F. A.M.A. Aldhuhouri, M. M. Al Obeidli, H. H. Leung

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we derive new summation identities involving the (products of) Fibonacci quaternions by the method of summation-by-parts. We apply our method to derive summation identities which involve the (products of) hyperFibonacci quater-nions. By using the method of generating functions, we derive convolution-sum identities for the Fibonacci quaternions. Finally, we derive binomial-sum identities for the Fibonacci quaternions by matrix method.

Original language	English
Pages (from-to)	13-37
Number of pages	25
Journal	Journal of Algebra and Applied Mathematics
Volume	19
Issue number	1
Publication status	Published - Mar 2021

Keywords

Binomial-sum identity
Fibonacci quaternions
Fibonacci sequence
Summation identity

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics
Computational Mathematics
Applied Mathematics

Cite this

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title = "Some summation identities for fibonacci quaternions and hyper-fibonacci quaternions∗",

abstract = "In this paper, we derive new summation identities involving the (products of) Fibonacci quaternions by the method of summation-by-parts. We apply our method to derive summation identities which involve the (products of) hyperFibonacci quater-nions. By using the method of generating functions, we derive convolution-sum identities for the Fibonacci quaternions. Finally, we derive binomial-sum identities for the Fibonacci quaternions by matrix method.",

keywords = "Binomial-sum identity, Fibonacci quaternions, Fibonacci sequence, Summation identity",

author = "Aldhuhouri, {F. A.M.A.} and {Al Obeidli}, {M. M.} and Leung, {H. H.}",

note = "Funding Information: by UAEU SURE+ grant (Grant no. 00003159) in the Publisher Copyright: {\textcopyright} SAS International Publications URL: www.sasip.net.",

year = "2021",

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AU - Aldhuhouri, F. A.M.A.

AU - Al Obeidli, M. M.

AU - Leung, H. H.

N1 - Funding Information: by UAEU SURE+ grant (Grant no. 00003159) in the Publisher Copyright: © SAS International Publications URL: www.sasip.net.

PY - 2021/3

Y1 - 2021/3

N2 - In this paper, we derive new summation identities involving the (products of) Fibonacci quaternions by the method of summation-by-parts. We apply our method to derive summation identities which involve the (products of) hyperFibonacci quater-nions. By using the method of generating functions, we derive convolution-sum identities for the Fibonacci quaternions. Finally, we derive binomial-sum identities for the Fibonacci quaternions by matrix method.

AB - In this paper, we derive new summation identities involving the (products of) Fibonacci quaternions by the method of summation-by-parts. We apply our method to derive summation identities which involve the (products of) hyperFibonacci quater-nions. By using the method of generating functions, we derive convolution-sum identities for the Fibonacci quaternions. Finally, we derive binomial-sum identities for the Fibonacci quaternions by matrix method.

KW - Binomial-sum identity

KW - Fibonacci quaternions

KW - Fibonacci sequence

KW - Summation identity

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ER -

Some summation identities for fibonacci quaternions and hyper-fibonacci quaternions^∗

Abstract

Keywords

ASJC Scopus subject areas

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