Corpus ID: 235829865

Rodrigues' descendants of a polynomial and Boutroux curves

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


On spectral polynomials of the Heun equation. I
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Nearest neighbor recurrence relations for multiple orthogonal polynomials
  • W. Assche
  • Mathematics, Computer Science
  • J. Approx. Theory
  • 2011
It is shown how the Christoffel–Darboux formula for multiple orthogonal polynomials can be obtained easily using this information and gives explicit examples involving multiple Hermite, Charlier, Laguerre, and Jacobi polynmials. Expand