A new set of special functions, which has a wide range of applications from number theory to integrability of nonlinear dynamical systems, is described. We study multiple orthogonal polynomials with respect to p > 1 weights satisfying Pearson's equation. In particular, we give a classification of multiple orthogonal polynomials with respect to classical weights, which is based on properties of the corresponding Rodrigues operators. We show that the multiple orthogonal polynomials in our classification satisfy a linear differential equation of order p + 1. We also obtain explicit formulas and recurrence relations for these polynomials.

Abstract. We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these polynomials. We can apply this result to three examples of multiple orthogonal polynomials, in particular Jacobi-Piñeiro, Laguerre I and the example associated with modified Bessel functions. We also discuss an application to Toeplitz matrices.

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