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Zeitschrift für Analysis und ihre Anwendungen

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Volume 17, Issue 4, 1998, pp. 963–977
DOI: 10.4171/ZAA/861

Published online: 1998-12-31

Explicit Calculation of Some Polynomials Introduced by W. Gautschi

H.-J. Fischer[1]

(1) Technische Universität Chemnitz, Germany

In his classical by now investigation of the numerical condition of methods for computing orthogonal polynomials from modified moments, Gautschi introduced some poly-nomials defined by the nodes and weights of a Gaussian quadrature formula for the measure of orthogonality. We show that these polynomials can be calculated explicitly for Chebyshev weights of first, second and third kinds.

Keywords: Numerical condition, orthogonal polynomials, modified moments, Chebyshev and Jacobi weights

Fischer H.-J.: Explicit Calculation of Some Polynomials Introduced by W. Gautschi. Z. Anal. Anwend. 17 (1998), 963-977. doi: 10.4171/ZAA/861