Orthogonality of Jacobi polynomials with general parameters

By Arno B. J. Kuijlaars, Andrei Martínez-Finkelshtein, R. Orive. 2003

85 citations recorded by the source corpus.

In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of contours in the plane. In all cases we show that the orthogonality conditions characterize the Jacobi polynomial $P_n^{(\alpha, \beta)}$ of degree $n$ up to a constant factor.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/883eb8d772c3eced1eb9f6a9c94271a48103fd62

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In Applied Mathematics

1. Andrei Martínez-Finkelshtein
2. Arno B. J. Kuijlaars
3. Alexei S. Zhedanov
4. Luc Vinet
5. Alexander I. Aptekarev
6. Maxim L. Yattselev
7. Paul M. Terwilliger
8. K. Mclaughlin

In Geometry and Topology

1. Andrei Martínez-Finkelshtein
2. Arno B. J. Kuijlaars
3. Alexei S. Zhedanov
4. Luc Vinet

Citations in the corpus

• A LIMIT q = −1 FOR THE BIG Q-JACOBI POLYNOMIALS (2012, background): “In this case the orthogonality relation can be rather complicated (see [13] for details).”
• Strong asymptotics for Jacobi polynomials with varying nonstandard parameters (2003, background): “See [ 20 ] for an overview of non-hermitian orthogonality properties of Jacobi polynomials with general parameters.”