A Generalization of Classical Symmetric Orthogonal Functions Using a Symmetric Generalization of Sturm-Liouville Problems
Classical Analysis and ODEs
2013-05-23 v1
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.
Keywords
Cite
@article{arxiv.1305.5156,
title = {A Generalization of Classical Symmetric Orthogonal Functions Using a Symmetric Generalization of Sturm-Liouville Problems},
author = {Mohammad Masjed-Jamei},
journal= {arXiv preprint arXiv:1305.5156},
year = {2013}
}
Comments
17 pages