Some summation identities for fibonacci quaternions and hyper-fibonacci quaternions

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)13-37
Number of pages25
JournalJournal of Algebra and Applied Mathematics
Issue number1
Publication statusPublished - Mar 2021


  • 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


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