Abstract
A recent paper of Swamy [4] contains eight finite sums. Three of these are sums discovered by Jennings [3] which express F (2p+1)n as a polynomial in F n, and F mn/F n as a polynomial in L n. Three are sums discovered by Filipponi [2] which express L mn as a polynomial in L n, and L 2qn as a polynomial in F n. The remaining two are sums discovered by Swamy which express F 2qn/L n as a polynomial in F n, and L (2q+1)n/L n as a polynomial in F n.
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References
Carlitz, L. “A Fibonacci Array.” The Fibonacci Quarterly, Vol. 1.2 (1963): pp. 17–27.
Filipponi, P. “Some Binomial Fibonacci Identities.” The Fibonacci Quarterly, Vol. 33.3 (1995): pp. 251–257.
Jennings, D. “Some Polynomial Identities for the Fibonacci and Lucas Numbers.” The Fibonacci Quarterly, Vol. 31.2 (1993): pp. 134–137.
Swamy, M.N.S. “On Certain Identities Involving Fibonacci and Lucas Numbers.” The Fibonacci Quarterly, Vol. 35.3 (1997): pp. 230–232.
Wilf, Herbert S. Generatingfunctionology. Boston-San Diego-New York: Academic Press, 1990.
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© 1999 Springer Science+Business Media Dordrecht
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Melham, R.S. (1999). On Certain Polynomials of Even Subscripted Lucas Numbers. In: Howard, F.T. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4271-7_25
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DOI: https://doi.org/10.1007/978-94-011-4271-7_25
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