Pseudo-Lucas Functions of Fractional Degree and Applications
Abstract
:1. Introduction
2. Basic Definitions
2.1. Recalling the Multivariate Lucas Polynomials
Integral Representations
3. The Multivariate Pseudo-Lucas Functions
3.1. Applications of the SKMP-L Functions
3.2. Applications of the FKMP-L Functions
4. A Recursion for the Coefficients of Orthogonal Polynomial Sets
5. The Case of Fractional Moments
6. Numerical Computations
6.1. Second Kind of Chebyshev Polynomial
6.2. Legendre Polynomial
6.3. Third Kind of Chebyshev Polynomial
6.4. Fourth Kind Chebyshev Polynomial
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Cesarano, C.; Natalini, P.; Ricci, P.E. Pseudo-Lucas Functions of Fractional Degree and Applications. Axioms 2021, 10, 51. https://doi.org/10.3390/axioms10020051
Cesarano C, Natalini P, Ricci PE. Pseudo-Lucas Functions of Fractional Degree and Applications. Axioms. 2021; 10(2):51. https://doi.org/10.3390/axioms10020051
Chicago/Turabian StyleCesarano, Clemente, Pierpaolo Natalini, and Paolo Emilio Ricci. 2021. "Pseudo-Lucas Functions of Fractional Degree and Applications" Axioms 10, no. 2: 51. https://doi.org/10.3390/axioms10020051
APA StyleCesarano, C., Natalini, P., & Ricci, P. E. (2021). Pseudo-Lucas Functions of Fractional Degree and Applications. Axioms, 10(2), 51. https://doi.org/10.3390/axioms10020051