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Orthogonal polynomials and Painlevé equations

Author: Walter van Assche
Publisher: Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018. ©2018
Series: Australian Mathematical Society lecture series, 27.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

The first detailed account of the relationships between Painleve equations and orthogonal polynomials. It gives clear examples as well as proofs, and there are exercises throughout to help the reader  Read more...

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Document Type: Book
All Authors / Contributors: Walter van Assche
ISBN: 9781108441940 1108441947
OCLC Number: 1004922287
Description: xii, 179 pages ; 23 cm.
Contents: Note continued: 4.1.Orthogonal polynomials with exponential weights --
4.2.Riemann-Hilbert problem for orthogonal polynomials --
4.3.Proof of the ladder operators --
4.4.A modification of the Laguerre polynomials --
4.5.Ladder operators for orthogonal polynomials on the linear lattice --
4.6.Ladder operators for orthogonal polynomials on a q-lattice --
5.Other semi-classical orthogonal polynomials --
5.1.Semi-classical extensions of Laguerre polynomials --
5.2.Semi-classical extensions of Jacobi polynomials --
5.3.Semi-classical extensions of Meixner polynomials --
5.4.Semi-classical extensions of Stieltjes --
Wigert and q-Laguerre polynomials --
5.5.Semi-classical bi-orthogonal polynomials on the unit circle --
5.6.Semi-classical extensions of Askey --
Wilson polynomials --
6.Special solutions of Painleve equations --
6.1.Rational solutions --
6.1.1.Painleve II --
6.1.2.Painleve III --
6.1.3.Painleve IV --
6.1.4.Painleve V --
6.1.5.Painleve VI Note continued: 6.2.Special function solutions --
6.2.1.Painleve II --
6.2.2.Painleve III --
6.2.3.Painleve IV --
6.2.4.Painleve V --
6.2.5.Painleve VI --
7.Asymptotic behavior of orthogonal polynomials near critical points --
7.1.Painleve I --
7.2.Painleve II --
7.3.Painleve III --
7.4.Painleve IV --
7.5.Painleve V --
7.6.Painleve VI.
Series Title: Australian Mathematical Society lecture series, 27.
Responsibility: Walter van Assche, Katholieke Universiteit Leuven, Belgium.

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