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Hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitely described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the parameters involved. We study the parameter dependence of orthogonality, square integrability and monotony of the eigenvalue sequence. The results obtained allow us to define certain systems of Gazeau-Klauder type coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural, unified way and also leads to new findings. [ABSTRACT FROM AUTHOR]

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. The equations considered are directly related to some Schrödinger type equations (Pöschl-Teller, Scarf, Morse, etc), and the special functions defined are related to the corresponding bound-state eigenfunctions. [ABSTRACT FROM AUTHOR]

An icosahedral quasicrystal can be regarded as a packing of copies of a well-defined atomic clusterC. On the other hand, by starting from any clusterCwith icosahedral symmetry we can define in terms of the strip projection method a quasiperiodic packing of copies ofC. The dimension of the superspace we have to use in this definition can be reduced by using the notion of multi-componentmodelset(a generalization of the notion of model set, proposed by Baake and Moody). [ABSTRACT FROM AUTHOR]