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On Polynomial Eigenfunctions of a Hypergeometric-Type Operator
Consider the operator where Q(x) is some fixed polynomial of degree k. One can easily see that σQ has exactly one polynomial eigenfunction Pn(x) in each degree n ≥ 0 and its eigenvalue λn,k equals (n + k)!/h!. A more intriguing fact is that all zeros of Pn(x) lie in …