Orthogonal polynomials, associated special functions and coherent states

Abstract. The Schrödinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The mathematical formulae occurring in the study of these quantum systems are consequences of some fundamental results from the theory of special functions. We present in a unified and explicit way the systems of orthogonal polynomials defined by hypergeometric-type equations, the associated special functions and corresponding systems of coherent states. This general formalism allows us to extend certain results known in the case of some particular potentials.