A Christoffel–Darboux formula for multiple orthogonal polynomials Original Research Article

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.