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On Salikhov's integral


Author: V. N. Sorokin
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 77 (2016), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2016, 107-126
MSC (2010): Primary 30E10; Secondary 30C85, 33C47, 11J82
DOI: https://doi.org/10.1090/mosc/254
Published electronically: November 28, 2016
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Abstract: We state a new interpolation problem, which we solve using Salikhov's integral. This was previously used in the theory of Diophantine approximations. We study the asymptotic behaviour of orthogonal polynomials related to this problem.


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Additional Information

V. N. Sorokin
Affiliation: Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia
Email: vnsormm@mech.math.msu.su

DOI: https://doi.org/10.1090/mosc/254
Keywords: Approximations of logarithms, Hermite--Pad\'e approximations, saddle-point method, algebraic functions and Riemann surfaces, equilibrium logarithmic potentials
Published electronically: November 28, 2016
Article copyright: © Copyright 2016 American Mathematical Society