A Christoffel-Darboux formula for multiple orthogonal polynomials

Details A Christoffel-Darboux formula for multiple orthogonal polynomials A Christoffel-Darboux formula for multiple orthogonal polynomials

2004-02-03

arxiv.org/abs/math/0402031v1

Journal of Approximation Theory 130 (2004), 188-200

Mathematics

Classical Analysis and ODEs

11 pages, no figures

Scientific paper

Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a Christoffel-Darboux formula for this kernel for general multiple orthogonal polynomials. In addition, we show that the formula can be written in terms of the solution of the Riemann-Hilbert problem for multiple orthogonal polynomials, which will be useful for asymptotic analysis.

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