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 Keldysh Institute preprints, 2017, 085 (Mi ipmp2301)

Strong asymptotics of Hermite–Pade approximants for the Nikishin system of Jacobi weights

V. G. Lysov

Abstract: The Hermite–Pade approximants for the Cauchy transforms of the Jacobi weights on one interval are considered. This system of functions forms a Nikishin system. The denominators of the approximants are known as Jacobi–Pineiro polynomials. For the case of two weights the integral representations are obtained, the weak asymptotics is investigated. For the diagonal indexes the strong asymptotics of the polynomials and the functions of the second kind is found. The classical saddle point method is used.

Keywords: Jacobi–Pineiro multiple orthogonal polynomials, Nikishin system, integral representations, generalized hypergeometric functions, strong asymptotics, saddle point method.

 Funding Agency Grant Number Russian Science Foundation 14-21-00025

DOI: https://doi.org/10.20948/prepr-2017-85

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Document Type: Preprint
UDC: 517.53

Citation: V. G. Lysov, “Strong asymptotics of Hermite–Pade approximants for the Nikishin system of Jacobi weights”, Keldysh Institute preprints, 2017, 085, 35 pp.

Citation in format AMSBIB
\Bibitem{Lys17} \by V.~G.~Lysov \paper Strong asymptotics of Hermite--Pade approximants for the Nikishin system of Jacobi weights \jour Keldysh Institute preprints \yr 2017 \papernumber 085 \totalpages 35 \mathnet{http://mi.mathnet.ru/ipmp2301} \crossref{https://doi.org/10.20948/prepr-2017-85}