A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape-invariant operators. These operators can be analysed together and the mathematical formalism we use can be extended in order to define other shape-invariant operators. All the shape-invariant operators considered are directly related to Schrödinger-type equations.
 A.F. Nikiforov, S.K. Suslov and V.B. Uvarov: Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991.
 N. Cotfas: “Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics”, Cent. Eur. J. Phys., Vol. 2, (2004), pp. 456–466. See also http://fpcm5.fizica.unibuc.ro/:_ncotfas.
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