Mehler-Heine asymptotics for multiple orthogonal polynomials (Q2832829)

Mehler-Heine asymptotics describe the behavior of Legendre and Jacobi polynomials near the endpoint of their interval of orthogonality, in terms of Bessel functions \(J_{\nu}(z)\). The author obtains Mehler-Heine asymptotics for some classical multiple orthogonal polynomials near the endpoint of the integrals of orthogonality. The important fact is that the weights for the multiple orthogonal polynomials have a common endpoint at \(0\), so the asymptotic behavior is in terms of a generalized Bessel function. The multiple orthogonal polynomials considered are the Jacobi-Angelesco, Jacobi-Pineiro polynomials and some polynomials associated with modified Bessel functions or Meijer G-functions.