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An Introduction to Orthogonal Polynomials

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Orthogonal Polynomials (AIMSVSW 2018)

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Abstract

In this introductory talk, we first revisit with proof for illustration purposes some basic properties of a specific system of orthogonal polynomials, namely the Chebyshev polynomials of the first kind. Then we define the notion of orthogonal polynomials and provide with proof some basic properties such as: The uniqueness of a family of orthogonal polynomials with respect to a weight (up to a multiplicative factor), the matrix representation, the three-term recurrence relation, the Christoffel-Darboux formula and some of its consequences such as the separation of zeros and the Gauss quadrature rules.

The research of the author was partially supported by the AIMS-Cameroon Research Allowance 2018–2019.

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Acknowledgements

The author would like to thank the anonymous reviewer for his careful reading of the manuscript and his many insightful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Higher Teachers’ Training College, University of Yaounde I, Yaounde, Cameroon

    Mama Foupouagnigni

  2. The African Institute for Mathematical Sciences, Limbe, Cameroon

    Mama Foupouagnigni

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  1. Mama Foupouagnigni
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Correspondence to Mama Foupouagnigni .

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Editors and Affiliations

  1. University of Yaoundé I, Yaoundé, Cameroon; African Institute for Mathematical Sciences, Limbe, Cameroon

    Mama Foupouagnigni

  2. Institute for Mathematics, University of Kassel, Kassel, Germany

    Wolfram Koepf

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Foupouagnigni, M. (2020). An Introduction to Orthogonal Polynomials. In: Foupouagnigni, M., Koepf, W. (eds) Orthogonal Polynomials. AIMSVSW 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36744-2_1

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