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arXiv · 1802.09708

Series solutions of Laguerre- and Jacobi-type differential equations in terms of orthogonal polynomials and physical applications

A. D. Alhaidari
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Abstract

We introduce two ordinary second-order linear differential equations of the Laguerre- and Jacobi-type. Solutions are written as infinite series of square integrable functions in terms of the Laguerre and Jacobi polynomials, respectively. The expansion coefficients of the series satisfy three-term recursion relations, which are solved in terms of orthogonal polynomials with continuous and/or discrete spectra. Most of these are well-known polynomials whereas few are not. We present physical applications of these differential equations in quantum mechanics.

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A. D. Alhaidari. 2018-02-27. Series solutions of Laguerre- and Jacobi-type differential equations in terms of orthogonal polynomials and physical applications. https://doi.org/10.1063/1.5027158

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