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A Family of New Generating Functions for the Chebyshev Polynomials, Based on Works by Laplace, Lagrange and Euler

Author

Listed:
  • Claude Brezinski

    (Laboratory Paul Painlevé, University of Lille, CNRS, UMR 8524, F-59000 Lille, France)

  • Michela Redivo-Zaglia

    (Department of Mathematics “Tullio Levi-Civita”, University of Padua, Via Trieste 63, 35121 Padua, Italy)

Abstract

Analyzing, developing and exploiting results obtained by Laplace in 1785 on the Fourier-series expansion of the function ( 1 − 2 α cos θ + α 2 ) − s , we obtain a family of new expansions and generating functions for the Chebyshev polynomials. A relation between the generating functions of the Chebyshev polynomials T n and the Gegenbauer polynomials C n ( 2 ) is given.

Suggested Citation

  • Claude Brezinski & Michela Redivo-Zaglia, 2024. "A Family of New Generating Functions for the Chebyshev Polynomials, Based on Works by Laplace, Lagrange and Euler," Mathematics, MDPI, vol. 12(5), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:751-:d:1350143
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