# Rodrigues' descendants of a polynomial and Boutroux curves

@inproceedings{Bgvad2021RodriguesDO, title={Rodrigues' descendants of a polynomial and Boutroux curves}, author={Rikard B{\o}gvad and Christian Hagg and Boris Z. Shapiro}, year={2021} }

Motivated by the classical Rodrigues’ formula, we study below the root asymptotic of the polynomial sequence R[αn],n,P (z) = d[αn]Pn(z) dz[αn] , n = 0, 1, . . . where P (z) is a fixed univariate polynomial, α is a fixed positive number smaller than degP , and [αn] stands for the integer part of αn. Our description of this asymptotic is expressed in terms of an explicit harmonic function uniquely determined by the plane rational curve emerging from the application of the saddle point method to… Expand

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