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- W2887072344 abstract "A second order polynomial sequence is of emph{Fibonacci-type} (emph{Lucas-type}) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Known examples of these type of sequences are: Fibonacci polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials. The emph{resultant} of two polynomials is the determinant of the Sylvester matrix and the emph{discriminant} of a polynomial $p$ is the resultant of $p$ and its derivative. We study the resultant, the discriminant, and the derivatives of Fibonacci-type polynomials and Lucas-type polynomials as well combinations of those two types. As a corollary we give explicit formulas for the resultant, the discriminant, and the derivative for the known polynomials mentioned above." @default.
- W2887072344 created "2018-08-22" @default.
- W2887072344 creator A5031307059 @default.
- W2887072344 creator A5062374923 @default.
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- W2887072344 date "2018-08-03" @default.
- W2887072344 modified "2023-09-27" @default.
- W2887072344 title "The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials" @default.
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