Polinômios de Romanovski-Routh
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Data
2022-03-29
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Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho estudamos características, propriedades e aplicações dos polinômios de Romanovski-Routh. Tais polinômios formam uma classe de polinômios ortogonais clássicos, ou seja, são soluções polinomiais de uma equação diferencial ordinária com coeficientes polinomiais chamada equação hipergeométrica. Compilamos resultados quanto a suas representações, ortogonalidade, zeros e aplicação à Mecânica Quântica. Apresentamos também duas famílias que constituem partições do conjunto de todos os polinômios de Romanovski-Routh, uma delas composta pelos polinômios complementares de Romanovski-Routh.
ln this work we study characteristics, properties and applications of Romanovski-Routh polynomials. These polynomials form a class of classical orthogonal polynomials, that is, they are polynomial solutions of an ordinary differential equation with polynomial coefficients called the hypergeometric equation. We compile results regarding their representations, orthogonality, zeros and application to Quantum Mechanics. We also present two families that constitute partitions of the set of ali Romanovski-Routh polynomials, one ot them tormed by the complementary Romanovski-Routh polynomials.
ln this work we study characteristics, properties and applications of Romanovski-Routh polynomials. These polynomials form a class of classical orthogonal polynomials, that is, they are polynomial solutions of an ordinary differential equation with polynomial coefficients called the hypergeometric equation. We compile results regarding their representations, orthogonality, zeros and application to Quantum Mechanics. We also present two families that constitute partitions of the set of ali Romanovski-Routh polynomials, one ot them tormed by the complementary Romanovski-Routh polynomials.
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Polinômios ortogonais, Equações hipergeométricas, Polinômios de Romanovski-Routh, Orthogonal polynomials, Hypergeometric equations, Romanovski-Routh polynomials