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.
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I would like to thank Gradimir Milovanović for comments and references.
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Reichel, L. (2014). Polynomials orthogonal on the semicircle. In: Brezinski, C., Sameh, A. (eds) Walter Gautschi, Volume 2. Contemporary Mathematicians. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7049-6_2
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DOI: https://doi.org/10.1007/978-1-4614-7049-6_2
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