On Fibonacci quaternions. (English) Zbl 1329.11016

Summary: 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 sum formulas for them.


11B39 Fibonacci and Lucas numbers and polynomials and generalizations
Full Text: DOI


[1] Horadam A.F.: Complex Fibonacci Numbers and Fibonacci Quaternions. Amer. Math. Monthly 70, 289–291 (1963) · Zbl 0122.29402
[2] Horadam A.F.: Quaternion Recurrence Relations. Ulam Quaterly 2, 23–33 (1993) · Zbl 0846.11013
[3] Iakin A.L.: Generalized Quaternions of Higher Order. The Fib. Quarterly 15, 343–346 (1977) · Zbl 0407.10014
[4] Iakin A.L.: Generalized Quaternions with Quaternion Components. The Fib. Quarterly 15, 350–352 (1977) · Zbl 0407.10015
[5] Iyer M.R.: A Note On Fibonacci Quaternions. The Fib. Quarterly 3, 225–229 (1969) · Zbl 0191.32701
[6] Swamy M.N.S.: On Generalized Fibonacci Quaternions. The Fib. Quarterly 5, 547–550 (1973) · Zbl 0281.10006
[7] Koshy T.: Fibonacci and Lucas Numbers with Applications. A Wiley-Interscience publication, U.S.A (2001) · Zbl 0984.11010
[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) · Zbl 1272.15016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.