Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials
Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials
Date
2023-09-15
Authors
Dionicio Peralta
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Abstract
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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Citation
Peralta, D., Quintana, Y., & Wani, S. A. (2023). Mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. Mathematics, 11(3920).