Geodesic
High-order recurrence relations, Hermite-Pad\'e approximation and Nikishin systems
Sbornik. Mathematics, Tome 209 (2018) no. 3, pp. 385-420

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The study of sequences of polynomials satisfying high-order recurrence relations is connected with the asymptotic behaviour of multiple orthogonal polynomials, the convergence properties of type II Hermite-Padé approximation and eigenvalue distribution of banded Toeplitz matrices. We present some results for the case of recurrences with constant coefficients which match what is known for the Chebyshev polynomials of the first kind. In particular, under appropriate assumptions, we show that the sequence of polynomials satisfies multiple orthogonality relations with respect to a Nikishin-type system of measures. Bibliography: 20 titles.
Keywords: high-order recurrence relation, Hermite-Padé approximation, multiple orthogonality, Nikishin system. 
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     author = {D. Barrios Rolan{\'\i}a and J. S. Geronimo and G. L\'opez Lagomasino},
     title = {High-order recurrence relations, {Hermite-Pad\'e} approximation and {Nikishin} systems},
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D. Barrios Rolanía; J. S. Geronimo; G. López Lagomasino. High-order recurrence relations, Hermite-Pad\'e approximation and Nikishin systems. Sbornik. Mathematics, Tome 209 (2018) no. 3, pp. 385-420. http://geodesic.mathdoc.fr/item/SM_2018_209_3_a4/