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Generalised Gaussian Fibonacci numbers

Published online by Cambridge University Press:  17 April 2009

S. Pethe  and
A.F. Horadam
S. Pethe
Affiliation:
Department of Mathematics, University of Malaya, Kuala Lumpur, Malaysia.
A.F. Horadam
Affiliation:
Department of Mathematics, Statistics and Computing Science, University of New England, Armidale, N.S.W. 2351, Australia.
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Abstract

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In this paper, generalised Gaussian Fibonacci numbers are defined and, using the recurrence relation satisfied by them, we obtain a number of summation identities involving the products of combinations of Fibonacci, Pell and Chebyshev polynomials.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 1 , February 1986 , pp. 37 - 48
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Berzsenyi, G., “Gaussian Fibonacci Numbers”, The Fibonacci Quarterly 15 (1977), 233–236.Google Scholar
[2]Harman, C.J., “Complex Fibonacci Numbers”, The Fibonacci Quarterly 19 (1981), 82–86.Google Scholar
[3]Horadam, A.F., “Complex Fibonacci Numbers and Fibonacci Quaternions”, Amer. Math. Monthly 70 (1963), 289–291.CrossRefGoogle Scholar
[4]Lucas, E., Théorie des nombres, Albert Blanchard, Paris, 1961.Google Scholar