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

Claude Brezinski and Michela Redivo-Zaglia ()
Additional contact information
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

Mathematics, 2024, vol. 12, issue 5, 1-10

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.

Keywords: orthogonal polynomials; expansions; generating functions; Legendre polynomials; Chebyshev polynomials; Gegenbauer polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/5/751/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/5/751/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:5:p:751-:d:1350143

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().