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An Introduction to Orthogonal Polynomials

  • Mama FoupouagnigniEmail author
Conference paper
  • 41 Downloads
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)

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.

Keywords

Orthogonal polynomials Differential equations Chebyshev polynomials Zeros 

Mathematics Subject Classification (2000)

Primary 33C45; Secondary 42C05 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics, Higher Teachers’ Training CollegeUniversity of Yaounde IYaoundeCameroon
  2. 2.The African Institute for Mathematical SciencesLimbeCameroon

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