Polynomial solutions for a class of second-order linear differential equations

被引：7

作者：

Saad, Nasser ^{[1
]}

Hall, Richard L. ^{[2
]}

Trenton, Victoria A. ^{[1
]}

机构：

[1] Univ Prince Edward Isl, Dept Math & Stat, Charlottetown, PE C1A 4P3, Canada

[2] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 226卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Linear differential equations; Orthogonal polynomials; Hypergeometric functions; Recursion relations; Weight functions; Polynomial solutions of differential equations; SHAPE-INVARIANT POTENTIALS; ORTHOGONAL POLYNOMIALS; SCHRODINGER-EQUATION; SOLVABLE POTENTIALS; SYSTEMS;

D O I：

10.1016/j.amc.2013.10.056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the polynomial solutions of the linear differential equation p(2)(x)y"+ p(1)(x)y' + p(0)(x)y = 0 where p(j)(x) is a jth-degree polynomial. We discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials p(j)(x). Special cases are related to known differential equations of mathematical physics. Classes of new soluble problems are exhibited. General results are obtained for weight functions and orthogonality relations. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：615 / 634

页数：20

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