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A basic class of symmetric orthogonal functions using the extended Sturm–Liouville theorem for symmetric functions
- Source :
-
Journal of Computational & Applied Mathematics . Jun2008, Vol. 216 Issue 1, p128-143. 16p. - Publication Year :
- 2008
-
Abstract
- Abstract: By using the extended Sturm–Liouville theorem for symmetric functions, we introduced a basic class of symmetric orthogonal polynomials (BCSOP) in a previous paper. The mentioned class satisfies a differential equation of the formand contains four main sequences of symmetric orthogonal polynomials. In this paper, again by using the mentioned theorem, we introduce a basic class of symmetric orthogonal functions (BCSOF) as a generalization of BCSOP and obtain its standard properties. We show that the latter class satisfies the equationin which is a free parameter and denotes eigenvalues corresponding to BCSOF. We then consider four sub-classes of defined orthogonal functions class and study their properties in detail. Since BCSOF is a generalization of BCSOP for , the four mentioned sub-classes respectively generalize the generalized ultraspherical polynomials, generalized Hermite polynomials and two other finite sequences of symmetric polynomials, which were introduced in the previous work. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 216
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 31559865
- Full Text :
- https://doi.org/10.1016/j.cam.2007.04.025