Wielomiany Fibonacciego stopnia k
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Fibonacci polynominals, Fibonacci numbers, Pell numbers, polynomial coefficientsAbstrakt
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.Downloads
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André, D.: 1876, Mémoire sur les combinaisons régulières et leurs applications, Ann. Sci. École Norm. Sup. 5(2), 155-1928.
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.
Hoggatt, V. E., Bicknell, M.: 1973, Generalized Fibonacci polynomials, Fibonacci Qartelly 11, 457-465.
Koshy, T.: 2001, Fibonacci and Lucas numbers with applications, Iohn Wiley & Sons, Inc.
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.
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