Advances in Applied Clifford Algebras

, Volume 22, Issue 2, pp 321–327 | Cite as

On Fibonacci Quaternions

  • Serpil HaliciEmail author


In this paper, we investigate the Fibonacci and Lucas quaternions. We give the generating functions and Binet formulas for these quaternions. Moreover, we derive some sums formulas for them.


Recurrence relations Fibonacci numbers quaternions 


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  1. 1.
    Horadam A.F.: Complex Fibonacci Numbers and Fibonacci Quaternions. Amer. Math. Monthly 70, 289–291 (1963)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Horadam A.F.: Quaternion Recurrence Relations. Ulam Quaterly 2, 23–33 (1993)MathSciNetGoogle Scholar
  3. 3.
    Iakin A.L.: Generalized Quaternions of Higher Order. The Fib. Quarterly 15, 343–346 (1977)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Iakin A.L.: Generalized Quaternions with Quaternion Components. The Fib. Quarterly 15, 350–352 (1977)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Iyer M.R.: A Note On Fibonacci Quaternions. The Fib. Quarterly 3, 225–229 (1969)MathSciNetGoogle Scholar
  6. 6.
    Swamy M.N.S.: On Generalized Fibonacci Quaternions. The Fib. Quarterly 5, 547–550 (1973)MathSciNetGoogle Scholar
  7. 7.
    Koshy T.: Fibonacci and Lucas Numbers with Applications. A Wiley-Interscience publication, U.S.A (2001)zbMATHCrossRefGoogle Scholar
  8. 8.
    Sangwine Stephen J., Ell Todd A., Nicolas Le Bihan: Fundamental Represantations and Algebraic Properties of Biquaternions or Complexified Quaternions. Adv. Appl. Clifford Algebras 21, 607–636 (2011)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Arts and SciencesSakarya UniversitySakaryaTurkey

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