Wielomiany Fibonacciego stopnia k

Authors

  • Jan Górowski Instytut Matematyki, Uniwersytet Pedagogiczny w Krakowie
  • Adam Łomnicki Instytut Matematyki, Uniwersytet Pedagogiczny w Krakowie

Keywords:

Fibonacci polynominals, Fibonacci numbers, Pell numbers, polynomial coefficients

Abstract

In this paper, we give formulas determining the Fibonacci polynomials of order k using the so-called generalized Newton symbols, i.e., the coefficients in the expansion of (1+z +z^2 +. . .+z^{k−1})n with respect to the powers of z.

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References

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Belbachir, H., Bouroubi, S., Khelladi, A.: 2008, Connection between ordinary multinominals, Fibonacci numbers, Bell polynominals and discrete uniform distribution, Annales Math. et Informaticae 35, 21-30.

Górowski, J., Łomnicki, A.: 2010, Tożsamości dla uogólnionych symboli Newtona, Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia III, 67-77.

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Philippou, A. N., Georghiou, C., Philippou, G. N.: 1983, Fibonacci polynomials of order k, multinomial expansions and probability, Internat. J. Math. Math. Sci. 6(3), 545-550.

Schork, M.: 2008, The r-generalized Fibonacci numbers and polynominals coefficients, Internat. J. Math. Science 3(21-24), 1157-1163.

Published

2017-07-05

How to Cite

Górowski, J., & Łomnicki, A. (2017). Wielomiany Fibonacciego stopnia k. Annales Universitatis Paedagogicae Cracoviensis | Studia Ad Didacticam Mathematicae Pertinentia, 6, 95–100. Retrieved from https://didacticammath.uken.krakow.pl/article/view/3662

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