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Construction of the Shifted Modified Gegenbauer Polynomials and Approximation

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  • Abdelhamid Rehouma
  • Hossein Jafari

Abstract

This article is concerned with deriving a new system of orthogonal polynomials, derived from the Gegenbauer polynomials, modified by affine transforms in variable, named shifted Gegenbauer polynomials. They appear as solutions of linear differential equation. We study orthogonality and extremal properties and minimization involving of shifted Gegenbauer polynomials. There are some important properties and certain identities and extremal properties involving both kernel polynomials derived of the shifted Gegenbauer polynomials. We have used mathematical induction to establish the relation between them. These kernel polynomials can be used to obtain the minimizing function and the minimum value by applying the obtained results for numerous definite integrals, including weight function of shifted Gegenbauer polynomials.MSC2020 Classification: 42C05, 33C45

Suggested Citation

  • Abdelhamid Rehouma & Hossein Jafari, 2025. "Construction of the Shifted Modified Gegenbauer Polynomials and Approximation," Advances in Mathematical Physics, Hindawi, vol. 2025, pages 1-11, December.
    • Handle: RePEc:hin:jnlamp:8278473
    DOI: 10.1155/admp/8278473
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