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.
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页码：223 / 254
页数：32
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