Planar orthogonal polynomials as Type II multiple orthogonal polynomials

摘要

We show that the planar orthogonal polynomials with/logarithmic singularities in the potential are the multiple orthogonal polynomials (Hermite-Pade polynomials) of Type II with 1 measures. We also find the ratio between the determinant of the moment matrix corresponding to the multiple orthogonal polynomials and the determinant of the moment matrix from the original planar measure.