The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights

  • Authors:

  • A. B. J. Kuijlaars;P. M. J. Tibboel

  • Affiliations:

  • Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium;Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

Quantified Score

Hi-index 7.29

Visualization

Abstract

We consider orthogonal polynomials {p"n","N(x)}"n"="0^~ on the real line with respect to a weight w(x)=e^-^N^V^(^x^) and in particular the asymptotic behaviour of the coefficients a"n","N and b"n","N in the three-term recurrence x@p"n","N(x)=@p"n"+"1","N(x)+b"n","N@p"n","N(x)+a"n","N@p"n"-"1","N(x). For one-cut regular V we show, using the Deift-Zhou method of steepest descent for Riemann-Hilbert problems, that the diagonal recurrence coefficients a"n","n and b"n","n have asymptotic expansions as n-~ in powers of 1/n^2 and powers of 1/n, respectively.