Extended Jacobi and Laguerre Functions and their Applications
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Abstract:
The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also these sequences form two new orthog- onal bases for the corresponding Hilbert spaces. Finally, the spectral and Rayleigh-Ritz methods are carry out using these basis functions to solve some examples. Our nu- merical results are compared with other existing results to con rm the eciency and accuracy of our method.
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Journal title
volume 13 issue 2
pages 143- 161
publication date 2018-10
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