New characterizations of classical orthogonal polynomials

被引：10

作者：

Kwon, KH

Littlejohn, LL

Yoo, BH

机构：

[1] KOREA ADV INST SCI & TECHNOL,DEPT MATH,TAEJON 305701,SOUTH KOREA

[2] UTAH STATE UNIV,DEPT MATH & STAT,LOGAN,UT 84322

[3] ANDONG NATL UNIV,DEPT MATH EDUC,ANDONG 760749,SOUTH KOREA

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 1996年 / 7卷 / 02期

关键词：

D O I：

10.1016/0019-3577(96)85090-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Classical orthogonal polynomials of Jacobi, Laguerre, Hermite, and Bessel are characterized as the only orthogonal polynomials (up to a linear change of variable) such that (i) (Bochner) they satisfy a second order differential equation of the form l(2)(x)y ''(x)+l(1)(x)y'(x) = lambda(n)y(x); and (ii) (Hahn) their derivatives of any fixed order are also orthogonal. Here, we give several new characterizations of classical orthogonal polynomials including extensions of the above two characterizations.

引用

页码：199 / 213

页数：15

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