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Calculation of associated functions for rational modified weight functions

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Abstract

Let\(\{ P_n \} _{n \in IN_0 }\) be a sequence of polynomials orthogonal with respect to a measure dω on the real line and\(\{ Q_n \} _{n \in IN_0 }\) the sequence of their associated functions (they are essentially the Hilbert transforms of these polynomials). We show how to get associated functions Q [m,l] n if the measure dω changes to\(\frac{{\Phi _m }}{{\varphi _l }}\), where Φm and ϕ l are polynomials of degree m resp.l.

The results can be used for example to construct Gaussian quadrature rules for rational modified weight functions.

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Authors and Affiliations

  1. Fernuniversität-GHS-Hagen, Fachbereich Mathematik, Postfach 940, W-5800, Hagen 1, Germany

    M. -R. Skrzipek

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  1. M. -R. Skrzipek
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Skrzipek, M.R. Calculation of associated functions for rational modified weight functions. Calcolo 30, 145–158 (1993). https://doi.org/10.1007/BF02576178

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  • DOI: https://doi.org/10.1007/BF02576178

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