Classical orthogonal polynomials: A functional approach |
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| Authors: | F. Marcellán A. Branquinho J. Petronilho |
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| Affiliation: | (1) Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III, 28913 Leganés-Madrid, Spain;(2) Departamento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal |
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| Abstract: | We characterize the so-called classical orthogonal polynomials (Hermite, Laguerre, Jacobi, and Bessel) using the distributional differential equation D( u)= u. This result is naturally not new. However, other characterizations of classical orthogonal polynomials can be obtained more easily from this approach. Moreover, three new properties are obtained. |
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| Keywords: | Primary 33C45 Secondary 33D45 |
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