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Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials

Author

Listed:
  • Dionisio Peralta

    (Instituto de Matemática, Facultad de Ciencias, Universidad Autónoma de Santo Domingo, Santo Domingo 10105, Dominican Republic)

  • Yamilet Quintana

    (Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, 28911 Madrid, Spain
    Instituto de Ciencias Matemáticas (ICMAT), Campus de Cantoblanco UAM, 28049 Madrid, Spain)

  • Shahid Ahmad Wani

    (Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Lavale, Pune 412115, Maharashtra, India)

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.

Suggested Citation

  • Dionisio Peralta & Yamilet Quintana & Shahid Ahmad Wani, 2023. "Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3920-:d:1240222
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    References listed on IDEAS

    as
    1. Pierpaolo Natalini & Angela Bernardini, 2003. "A generalization of the Bernoulli polynomials," Journal of Applied Mathematics, Hindawi, vol. 2003, pages 1-9, January.
    2. Tom Cuchta & Rebecca Luketic, 2021. "Discrete Hypergeometric Legendre Polynomials," Mathematics, MDPI, vol. 9(20), pages 1-10, October.
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