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Mehler-Heine asymptotics for multiple orthogonal polynomials. (English) Zbl 1355.33014
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.

##### MSC:
 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
DLMF
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