### Abstract

In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight (Formula Presented) on (−1; 1), k > 1, and verify a conjecture of A. Magnus for these coefficients. We use Riemann{Hilbert/steepest-descent methods, but not in the standard way as there is no known parametrix for the Riemann-Hilbert problem in a neighborhood of the logarithmic singularity at x = 1.

Original language | English (US) |
---|---|

Article number | 056 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 14 |

DOIs | |

State | Published - Jun 12 2018 |

### Fingerprint

### Keywords

- Orthogonal polynomials
- Recurrence coefficients
- Riemann-Hilbert problems
- Steepest descent method

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

**Asymptotics of polynomials orthogonal with respect to a logarithmic weight.** / Conway, Thomas Oliver; Deift, Percy.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Asymptotics of polynomials orthogonal with respect to a logarithmic weight

AU - Conway, Thomas Oliver

AU - Deift, Percy

PY - 2018/6/12

Y1 - 2018/6/12

N2 - In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight (Formula Presented) on (−1; 1), k > 1, and verify a conjecture of A. Magnus for these coefficients. We use Riemann{Hilbert/steepest-descent methods, but not in the standard way as there is no known parametrix for the Riemann-Hilbert problem in a neighborhood of the logarithmic singularity at x = 1.

AB - In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight (Formula Presented) on (−1; 1), k > 1, and verify a conjecture of A. Magnus for these coefficients. We use Riemann{Hilbert/steepest-descent methods, but not in the standard way as there is no known parametrix for the Riemann-Hilbert problem in a neighborhood of the logarithmic singularity at x = 1.

KW - Orthogonal polynomials

KW - Recurrence coefficients

KW - Riemann-Hilbert problems

KW - Steepest descent method

UR - http://www.scopus.com/inward/record.url?scp=85050344342&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050344342&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2018.056

DO - 10.3842/SIGMA.2018.056

M3 - Article

AN - SCOPUS:85050344342

VL - 14

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 056

ER -