Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials Articles uri icon

publication date

  • September 2023

start page

  • 1

end page

  • 16


  • 18


  • 11

International Standard Serial Number (ISSN)

  • 2227-7390


  • 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.


  • Mathematics


  • gegenbauer polynomials; generalized bernoulli polynomials; hypergeometric bernoulli polynomials