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https://hdl.handle.net/10316/112201
Title: | Classical Orthogonal Polynomials Revisited | Authors: | Castillo, K. Petronilho, J. |
Keywords: | Moment linear functionals; classical orthogonal polynomials; algebraic theory of orthogonal polynomials | Issue Date: | 2023 | Publisher: | Springer Nature | Serial title, monograph or event: | Results in Mathematics | Volume: | 78 | Issue: | 4 | Abstract: | This manuscript contains a small portion of the algebraic theory of orthogonal polynomials developed by Maroni and their applicability to the study and characterization of the classical families, namely Hermite, Laguerre, Jacobi, and Bessel polynomials. It is presented a cyclical proof of some of the most relevant characterizations, particularly those due to Al-Salam and Chihara, Bochner, Hahn, Maroni, and McCarthy. Two apparently new characterizations are also added. Moreover, it is proved through an equivalence relation that, up to constant factors and affine changes of variables, the four families of polynomials named above are the only families of classical orthogonal polynomials. | URI: | https://hdl.handle.net/10316/112201 | ISSN: | 1422-6383 1420-9012 |
DOI: | 10.1007/s00025-023-01934-2 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais I&D CMUC - Artigos em Revistas Internacionais |
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