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arXiv · 1305.5156

A Generalization of Classical Symmetric Orthogonal Functions Using a Symmetric Generalization of Sturm-Liouville Problems

Mohammad Masjed-Jamei
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Abstract

In this paper, usual Sturm-Liouville problems are extended for symmetric functions so that the corresponding solutions preserve the orthogonality property. Two basic examples, which are special cases of a generalized Sturm-Liouville problem, are then introduced. First example generalizes the associated Legendre functions having extensive applications in physics and the second example introduces a generic differential equation with various sub-cases that have orthogonal solutions. For instance, this generic equation possesses a symmetric differential equation containing a basic solution of symmetric orthogonal polynomials.

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Mohammad Masjed-Jamei. 2013-05-22. A Generalization of Classical Symmetric Orthogonal Functions Using a Symmetric Generalization of Sturm-Liouville Problems. https://doi.org/10.1080/10652460701510949

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