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The classical sets of orthogonal polynomials of Jacobi, Laguerre, and Hermite satisfy second order differential equations, and also have the property that their derivatives form orthogonal systems. There is a fourth class of polynomials with these two properties, and similar in other ways to the other three classes, which has hitherto been little studied. We call these the Bessel polynomials because of their close relationship with the Bessel functions of half-integral order. They are orthogonal, but not in quite the same sense as the other three systems. The Bessel polynomials satisfy:
Krall et al. (Sat,) studied this question.
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