Abstract
We characterize the so-called classical orthogonal polynomials (Hermite, Laguerre, Jacobi, and Bessel) using the distributional differential equation D(φu)=ψu. 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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Marcellán, F., Branquinho, A. & Petronilho, J. Classical orthogonal polynomials: A functional approach. Acta Appl Math 34, 283–303 (1994). https://doi.org/10.1007/BF00998681
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DOI: https://doi.org/10.1007/BF00998681