Ladder operators and differential equations for multiple orthogonal polynomials

Details Ladder operators and differential equations for multiple orthogonal polynomials Ladder operators and differential equations for multiple orthogonal polynomials

2012-04-23

arxiv.org/abs/1204.5058v1

Mathematics

Classical Analysis and ODEs

28 pages

Scientific paper

In this paper, we obtain the ladder operators and associated compatibility conditions for the type I and the type II multiple orthogonal polynomials. These ladder equations extend known results for orthogonal polynomials and can be used to derive the differential equations satisfied by multiple orthogonal polynomials. Our approach is based on Riemann-Hilbert problems and the Christoffel-Darboux formula for multiple orthogonal polynomials, and the nearest-neighbor recurrence relations. As an illustration, we give several explicit examples involving multiple Hermite and Laguerre polynomials, and multiple orthogonal polynomials with exponential weights and cubic potentials.

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