Polynomials orthogonal on the semicircle

  • Lothar Reichel
Chapter
Part of the Contemporary Mathematicians book series (CM)

Abstract

In two papers, jointly with Henry J. Landau and Gradimir V. Milovanović, Walter Gautschi investigates polynomials that are orthogonal with respect to a non-Hermitian inner product defined on the upper half of the unit circle in the complex plane. For special choices of the weight function, these polynomials are related to Jacobi polynomials. Their recurrence relation and properties of their zeros are investigated, and applications to Gauss quadrature are explored. We first discuss the importance of orthogonal polynomials that satisfy recurrence relations with few terms, and then focus on the special properties of orthogonal polynomials on the semicircle.

Notes

Acknowledgement

I would like to thank Gradimir Milovanović for comments and references.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Lothar Reichel
    • 1
  1. 1.Department of Mathematical SciencesKent State UniversityKentUSA

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