Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function

Percy Deift, Mateusz Piorkowski

Research output: Contribution to journalArticlepeer-review


We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure (formula presented). The asymptotic formula confirms a special case of a conjecture by Magnus and extends earlier results by Conway and one of the authors. The proof relies on the Riemann–Hilbert method. The main difficulty in applying the method to the problem at hand is the lack of an appropriate local parametrix near the logarithmic singularity at x = +1.

Original languageEnglish (US)
Article number004
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
StatePublished - 2024


  • orthogonal polynomials
  • recurrence coefficientsteepest descent method
  • Riemann–Hilbert problems

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


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