# An asymptotic formula for polynomials orthonormal with respect to a varying weight. II

## Abstract

This paper gives a proof of the theorem announced by the authors in the preceding paper with the same title. The theorem states that asymptotically the behaviour of the polynomials which are orthonormal with respect to the varying weight e{sup −2nQ(x)}p{sub g}(x)/√(∏{sub j=1}{sup 2p}(x−e{sub j})) coincides with the asymptotic behaviour of the Nuttall psi-function, which solves a special boundary-value problem on the relevant hyperelliptic Riemann surface of genus g=p−1. Here e{sub 1}

- Authors:

- Steklov Mathematical Institute of Russian Academy of Sciences (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22364895

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 9; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; BOUNDARY-VALUE PROBLEMS; CALCULATION METHODS; POLYNOMIALS; RIEMANN SHEET

### Citation Formats

```
Komlov, A V, and Suetin, S P.
```*An asymptotic formula for polynomials orthonormal with respect to a varying weight. II*. United States: N. p., 2014.
Web. doi:10.1070/SM2014V205N09ABEH004420.

```
Komlov, A V, & Suetin, S P.
```*An asymptotic formula for polynomials orthonormal with respect to a varying weight. II*. United States. doi:10.1070/SM2014V205N09ABEH004420.

```
Komlov, A V, and Suetin, S P. Tue .
"An asymptotic formula for polynomials orthonormal with respect to a varying weight. II". United States.
doi:10.1070/SM2014V205N09ABEH004420.
```

```
@article{osti_22364895,
```

title = {An asymptotic formula for polynomials orthonormal with respect to a varying weight. II},

author = {Komlov, A V and Suetin, S P},

abstractNote = {This paper gives a proof of the theorem announced by the authors in the preceding paper with the same title. The theorem states that asymptotically the behaviour of the polynomials which are orthonormal with respect to the varying weight e{sup −2nQ(x)}p{sub g}(x)/√(∏{sub j=1}{sup 2p}(x−e{sub j})) coincides with the asymptotic behaviour of the Nuttall psi-function, which solves a special boundary-value problem on the relevant hyperelliptic Riemann surface of genus g=p−1. Here e{sub 1}},

doi = {10.1070/SM2014V205N09ABEH004420},

journal = {Sbornik. Mathematics},

number = 9,

volume = 205,

place = {United States},

year = {Tue Sep 30 00:00:00 EDT 2014},

month = {Tue Sep 30 00:00:00 EDT 2014}

}

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