The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlev, Equation

被引：42

作者：

Clarkson, Peter A. ^{[1
]}

Jordaan, Kerstin ^{[2
]}

机构：

[1] Univ Kent, Sch Math Stat & Actuarial Sci, Canterbury CT2 7NF, Kent, England

[2] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa

来源：

CONSTRUCTIVE APPROXIMATION | 2014年 / 39卷 / 01期

关键词：

Semiclassical orthogonal polynomials; Recurrence coefficients; Painleve equations; Wronskians; Parabolic cylinder functions; Hamiltonians; ORTHOGONAL POLYNOMIALS; DIFFERENTIAL-EQUATIONS; RECURRENCE COEFFICIENTS; MATRIX MODELS; TODA CHAIN; TRANSFORMATIONS; HAMILTONIANS; 2ND-ORDER; ENSEMBLES; SYSTEMS;

D O I：

10.1007/s00365-013-9220-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a semiclassical Laguerre weight and classical solutions of the fourth Painlev, equation. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of parabolic cylinder functions that arise in the description of special function solutions of the fourth Painlev, equation.

引用

页码：223 / 254

页数：32

共 50 条

[1] The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation
Peter A. Clarkson
Kerstin Jordaan
Constructive Approximation, 2014, 39 : 223 - 254
[2] Rational solutions of the fifth Painlevé equation. Generalized Laguerre polynomials
Clarkson, Peter A.
Dunning, Clare
STUDIES IN APPLIED MATHEMATICS, 2024, 152 (01) : 453 - 507
[3] Relationship between Jacobi, Laguerre and Hermite polynomials
Feldheim, E
ACTA MATHEMATICA, 1943, 75 (01) : 117 - 128
[4] A limit relationship between Laguerre and Hermite polynomials
Chen, KY
Srivastava, HM
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2005, 16 (01) : 75 - 80
[5] The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painleve equation
Filipuk, Galina
Van Assche, Walter
Zhang, Lun
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (20)
[6] Asymptotic forms of solutions to the fourth Painlevé equation
A. D. Bruno
I. V. Goryuchkina
Doklady Mathematics, 2008, 78 : 868 - 873
[7] An Ultradiscrete Matrix Version of the Fourth Painlevé Equation
Chris M. Field
Chris M. Ormerod
Advances in Difference Equations, 2007
[8] Asymptotic forms of solutions to the fourth Painlev, equation
Bruno, A. D.
Goryuchkina, I. V.
DOKLADY MATHEMATICS, 2008, 78 (03) : 868 - 873
[9] Classification of Real Solutions of the Fourth Painlevé Equation
Schiff, Jeremy
Twiton, Michael
MATHEMATICS, 2024, 12 (03)
[10] DISCRETE PAINLEVE EQUATIONS FOR RECURRENCE COEFFICIENTS OF SEMICLASSICAL LAGUERRE POLYNOMIALS
Boelen, Lies
Van Assche, Walter
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (04) : 1317 - 1331

← 1 2 3 4 5 →