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Novel properties of Fibonacci and Lucas polynomials

Published online by Cambridge University Press:  24 October 2008

F. J. Galvez  and
J. S. Dehesa
F. J. Galvez
Affiliation:
Dpto. de Física Teórica, Facultad de Ciencias, Universidad de Granada, Spain
J. S. Dehesa
Affiliation:
Dpto. de Física Nuclear, Facultad de Ciencias, Universidad de Granada, Spain
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Abstract

Average or global spectral properties of the Fibonacci and Lucas polynomials recently introduced in the theory of one-dimensional Ising chains are investigated. In addition, several partial sums of these polynomials are shown to have a compact form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 159 - 164
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Basin, S.. An application of continuants. Math. Mag. 37 (1964), 83–91.CrossRefGoogle Scholar
[2]Case, K. M.. Sum rules for zeros of polynomials. I. J. Math. Phys. 21 (1980), 702–708.CrossRefGoogle Scholar
[3]Doman, B. G. S. and Williams, J. K.. Fibonacci and Lucas polynomials. Math. Proc. Cambridge Philos. Soc. 90 (1981), 385–387.CrossRefGoogle Scholar
[4]Hansen, E.. Sums of functions satisfying recursion relations. Amer. Math. Monthly 88 (1981), 676–679.CrossRefGoogle Scholar
[5]Galvez, F. J. and Dehesa, J. S.. Some open problems of generalized Bessel polynomials. J. Phys. A 17 (1984).Google Scholar
[6]Lucas, E.. Theorie des nombres (Gauthier–Villars, 1891).Google Scholar
[7]Raghavacharyuxu, I. V. V. and Tekumalla, A. R.. Solution of the difference equations of generalized Lucas polynomials. J. Math. Phys. 13 (1972), 321–324.CrossRefGoogle Scholar
[8]Riordan, J.. An Introduction to Combinatorial Analysis (Wiley, 1958).Google Scholar
[9]Williams, J. K.. Ground state properties of frustrated Ising chains. J. Phys. C 14 (1981), 4095–4107.CrossRefGoogle Scholar