Admissibility condition for exceptional Laguerre polynomials

被引：16

作者：

Duran, Antonio J. ^{[1
]}

Perez, Mario ^{[2
,3
]}

机构：

[1] Univ Seville, Dept Anal Matemat, E-41080 Seville, Spain

[2] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

[3] Univ Zaragoza, IUMA, E-50009 Zaragoza, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 424卷 / 02期

关键词：

Orthogonal polynomials; Exceptional orthogonal polynomials; Differential operators; Laguerre polynomials;

D O I：

10.1016/j.jmaa.2014.11.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a necessary and sufficient condition for the integrability of the weight associated to the exceptional Laguerre polynomials. This condition is very much related to the fact that the associated second order differential operator has no singularities in (0, +infinity). (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1042 / 1053

页数：12

共 17 条

[1]

[Anonymous], 1953, Higher Transcendental Functions

[2] On sturm-liouville polynomial systems [J].

Bochner, S .

MATHEMATISCHE ZEITSCHRIFT, 1929, 29 :730-736

[3] Exceptional Meixner and Laguerre orthogonal polynomials [J].

Duran, Antonio J. .

JOURNAL OF APPROXIMATION THEORY, 2014, 184 :176-208

[4] Exceptional Charlier and Hermite orthogonal polynomials [J].

Duran, Antonio J. .

JOURNAL OF APPROXIMATION THEORY, 2014, 182 :29-58

[5]

Erdelyi A., 1953, Higher Transcendental Functions

[6] Exceptional orthogonal polynomials and the Darboux transformation [J].

Gomez-Ullate, D. ;

Kamran, N. ;

Milson, R. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (43)

[7] Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials [J].

Gomez-Ullate, David ;

Grandati, Yves ;

Milson, Robert .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (01)

[8] An extension of Bochner's problem: Exceptional invariant subspaces [J].

Gomez-Ullate, David ;

Kamran, Niky ;

Milson, Robert .

JOURNAL OF APPROXIMATION THEORY, 2010, 162 (05) :987-1006

[9] An extended class of orthogonal polynomials defined by a Sturm-Liouville problem [J].

Gomez-Ullate, David ;

Kamran, Niky ;

Milson, Robert .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 359 (01) :352-367

[10] Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials [J].

Grandati, Y. ;

Quesne, C. .

JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (07)

← 1 2 →