Pseudo-Lucas Functions of Fractional Degree and Applications

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 appli...

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Bibliographic Details
Published in:Axioms 2021, Vol.10 (2), p.51
Main Authors: Cesarano, Clemente, Natalini, Pierpaolo, Ricci, Paolo
Format: Article
Language:English
Subjects:
Applied mathematics
Chebyshev approximation
Eigenvalues
fractional newton sum rules
generalized lucas functions of fractional degree
integral representations
matrix roots
orthogonal polynomials
Polynomials
recurrence relations
Sum rules
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms10020051