Instituto de Matemática

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Browsing Instituto de Matemática by Author "Dionisio Peralta Pérez"

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    Mixed-type hypergeometric Bernoulli-Gegenbauer Polynomials
    (2023) Dionisio Peralta Pérez
    In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and Gegenbauer polynomials. We focus our attention on some algebraic and differential properties of this class of polynomials, including its explicit expressions, derivative formulas, matrix representations, matrix-inversion formulas, and other relations connecting it with the hypergeometric Bernoulli polynomials. Furthermore, we show that unlike the hypergeometric Bernoulli polynomials and Gegenbauer polynomials, the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials do not fulfill either Hanh or Appell conditions.
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    Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials
    (2023-09-15) Dionisio Peralta Pérez
    In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli– Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and Gegenbauer polynomials. We focus our attention on some algebraic and differential properties of this class of polynomials, including its explicit expressions, derivative formulas, matrix representations, matrix-inversion formulas, and other relations connecting it with the hypergeometric Bernoulli polynomials. Furthermore, we show that unlike the hypergeometric Bernoulli polynomials and Gegenbauer polynomials, the mixed-type hypergeometric Bernoulli– Gegenbauer polynomials do not fulfill either Hanh or Appell conditions.
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    Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials: some properties
    (2024-11-06) Dionisio Peralta Pérez
    We consider the novel family of the mixed-type hypergeometric Bernoulli-Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and Gegenbauer polynomials. We collect some recent results concerning algebraic and differential properties of this class of polynomials and use some them to deduce an ordinary differential equation satisfied by these polynomials. Some numerical illustrative examples about the behavior of the zeros of these polynomials are given.