Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials: some properties

Dionisio Peralta; Yamilet Quintana

doi:10.2478/caim-2024-0018

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Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials: some properties

Communications in Applied and Industrial Mathematics

Volume 15 (2024): Issue 1 (January 2024)

By: Dionisio Peralta and Yamilet Quintana

Open Access

|Nov 2024

Abstract

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.

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Articles in this issue

DOI: https://doi.org/10.2478/caim-2024-0018 | Journal eISSN: 2038-0909

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Language: English

Page range: 123 - 136

Submitted on: Sep 26, 2024

Accepted on: Nov 1, 2024

Published on: Nov 7, 2024

Published by: Italian Society for Applied and Industrial Mathemathics

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Gegenbauer polynomials,

generalized Bernoulli polynomials,

hypergeometric Bernoulli polynomials,

operational methods

Related subjects:

Mathematics,

Numerical and computational mathematics,

Applied mathematics

© 2024 Dionisio Peralta, Yamilet Quintana, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 15 (2024): Issue 1 (January 2024)