### Abstract

We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e^{-Q(x)}dx on the real line, where Q(x) = Σ^{2m}_{k=0}q_{kxk}, q_{2m} > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert problem following [22, 23]. We employ the steepest-descent-type method introduced in [18] and further developed in [17, 19] in order to obtain uniform Plancherel-Rotach-type asymptotics in the entire complex plane, as well as asymptotic formulae for the zeros, the leading coefficients, and the recurrence coefficients of the orthogonal polynomials.

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

Pages (from-to) | 1491-1552 |

Number of pages | 62 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 52 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1999 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Strong asymptotics of orthogonal polynomials with respect to exponential weights'. Together they form a unique fingerprint.

## Cite this

*Communications on Pure and Applied Mathematics*,

*52*(12), 1491-1552. https://doi.org/10.1002/(sici)1097-0312(199912)52:12<1491::aid-cpa2>3.0.co;2-%23