: In a recent article, the first and second kinds of multivariate Chebyshev polynomials of fractional degree, and the relevant integral repesentations, have been studied. In this article, we introduce the first and second kinds of pseudo-Lucas functions of fractional degree, and we show possible applications of these new functions. For the first kind, we compute the fractional Newton sum rules of any orthogonal polynomial set starting from the entries of the Jacobi matrix. For the second kind, the representation formulas for the fractional powers of a r × r matrix, already introduced by using the pseudo-Chebyshev functions, are extended to the Lucas case.

Pseudo-Lucas Functions of Fractional Degree and Applications

Cesarano C;
2021-01-01

Abstract

: In a recent article, the first and second kinds of multivariate Chebyshev polynomials of fractional degree, and the relevant integral repesentations, have been studied. In this article, we introduce the first and second kinds of pseudo-Lucas functions of fractional degree, and we show possible applications of these new functions. For the first kind, we compute the fractional Newton sum rules of any orthogonal polynomial set starting from the entries of the Jacobi matrix. For the second kind, the representation formulas for the fractional powers of a r × r matrix, already introduced by using the pseudo-Chebyshev functions, are extended to the Lucas case.
2021
orthogonal polynomials
integral representations
ogeneralized lucas functions of fractional degree
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14086/1733
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