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arXiv · 1311.0188

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

Nasser Saad·Richard L. Hall·Victoria A. Trenton
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Abstract

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 $j^{\rm th}$-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.

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Nasser Saad, Richard L. Hall, Victoria A. Trenton. 2013-11-01. Polynomial solutions for a class of second-order linear differential equations. https://arxiv.org/abs/1311.0188

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