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Fibonacci and Lucas polynomials

Published online by Cambridge University Press:  24 October 2008

B. G. S. Doman  and
J. K. Williams
B. G. S. Doman
Affiliation:
University of Liverpool
J. K. Williams
Affiliation:
University of Liverpool
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Extract

The Fibonacci and Lucas polynomials Fn(z) and Ln(z) are denned. These reduce to the familiar Fibonacci and Lucas numbers when z = 1. The polynomials are shown to satisfy a second order linear difference equation. Generating functions are derived, and also various simple identities, and relations with hypergeometric functions, Gegenbauer and Chebyshev polynomials.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 3 , November 1981 , pp. 385 - 387
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Carlson, B. C.Special functions of applied mathematics (Academic Press, New York, 1977).Google Scholar
(2)Williams, J. K.Ground State Properties of frustrated Ising Chains. J. Phys. C 14 (1981) in press.CrossRefGoogle Scholar