Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation
Author
Juan F. Manas-Manas, Juan J. Moreno-Balcazar
Title
Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation
Description
The Sobolev orthogonal polynomials, which are orthogonal with respect to an inner product involving derivatives, are nonstandard orthogonal polynomials that has been developed along the last 40 years. The local asymptotics of these polynomials can be described by the Mehler-Heine formulae, which connect the polynomials with the Bessel functions of the first kind. Obtaining this type of asymptotics requires many calculations. Hence, we construct this algorithm that allows to compute the corresponding Mehler-Heine formulae automatically. Theoretical details, applications and examples are shown in "Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation", East Asian J. Appl. Math. 12(3) (2022), pp. 535-563, doi: 10.4208/eajam.240221.130921.
Category
Academic Articles & Supplements
Keywords
Sobolev orthogonal polynomials, asymptotics, Mehler-Heine formulae
URL
http://www.notebookarchive.org/2022-06-amlp3fh/
DOI
https://notebookarchive.org/2022-06-amlp3fh
Date Added
2022-06-23
Date Last Modified
2022-06-23
File Size
322. kilobytes
Supplements
Rights
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This file contains supplementary data for Juan F. Mañas-Mañas and Juan J. Moreno-Balcázar, “Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation,” East Asian J. Appl. Math., 12(3) (2022), pp. 535–563. https://doi.org/10.4208/eajam.240221.130921.
Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation
Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation
Juan F. Mañas-Mañas and Juan J. Moreno-Balcázar
The Sobolev orthogonal polynomials, which are orthogonal with respect to an inner product involving derivatives, are nonstandard orthogonal polynomials that has been developed along the last 40 years. The local asymptotics of these polynomials can be described by the Mehler-Heine formulae, which connect the polynomials with the Bessel functions of the first kind. Obtaining this type of asymptotics requires many calculations. Hence, we construct this algorithm that allows to compute the corresponding Mehler-Heine formulae automatically.
(*IFYOUFINDSOMEBUG,PLEASECONTACTUS(jmm939@ual.esorbalcazar@ual.es).*)selection1=ChoiceDialogStyleTraditionalForm"This program provides the limit function in the Mehler-Heine formula for the sequence of orthonormal polynomials with respect to the varying inner productf,g=∫f(x)g(x)μ+(c)(c).Please, choose between the general case (giving the so-called ℯ ) and the preloaded cases (Laguerre, Jacobi, generalized Freud).",FontSize12,{Style["General case",FontSize12]1,Style["Preloaded cases",FontSize12]2};
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Cite this as: Juan F. Manas-Manas, Juan J. Moreno-Balcazar, "Sobolev Orthogonal Polynomials: Asymptotics and Symbolic Computation" from the Notebook Archive (2022), https://notebookarchive.org/2022-06-amlp3fh
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