SOME CLASSES OF GENERALIZED MinMax POLYNOMIALS
Keywords:
Pell numbers, Modified Pell numbers, MinMax numbers, Pell-Lucas numbers, Recurrence relations, Explicit representations, Algebraic polynomials, MinMax polynomials, Fibonacci polynomials, Lucas polynomialsAbstract
The so-called MinMax numbers {Mn} and their subsidiary numbers {Nn} for the Pell numbers {Pn} were studied by (for example) A.F. Horadam [3]. These MinMax numbers {Mn} are positive integers which are the minimal and maximal representations by means of the Pell numbers. Analogous results for the MinMax numbers {Dn} and their subsidiary numbers {Rn}, and for the modified Pell numbers {qn}, are obtained in [3], Qn := 2qn being the Pell-Lucas numbers. A.F. Horadam [4], on the other hand, expanded this MinMax number system to the algebraic polynomials {Mn(x)}, {Nn(x)}, {Dn(x)} and {Rn(x)}. Our aim in this paper is to investigate results, which are similar to those in [4], but which hold true instead for the following generalized sequences of polynomials:
{Pn,m(x)} and {Qn,m(x)} (m ∈ \(\mathbb{N}\) ; n ∈ \(\mathbb{N}\) ∪ {0}),
N being the set of positive integers.
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Copyright (c) 2014 H.M. Srivastava, Gospava B. Djordjevi´c
This work is licensed under a Creative Commons Attribution 4.0 International License.
L'opera è pubblicata sotto Licenza Creative Commons Attribuzione 4.0 Internazionale (CC-BY)
