Titlebook: Special Functions 2000: Current Perspective and Future Directions; Joaquin Bustoz,Mourad E. H. Ismail,Sergei K. Suslo Book 2001 Kluwer Aca

Crayon

The Bochner-Krall Problem: Some New Perspectives,r. We survey some recent work on this problem. An important issue is to extend the problem by allowing for a doubly infinite three-term recursion relation, instead of a semi-infinite one. In this way, the problem gets connected with the associated classical orthogonal polynomials, the Darboux factor

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antiquated

The Associated Classical Orthogonal Polynomials,d by .., ..and .., . being the association parameter. Starting with examples where such polynomials occur in a natural way some of the well-known theories of how to determine their measures of orthogonality are discussed. The highest level of the family of classical orthogonal polynomials, namely, t

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tympanometry

The Factorization Method, Self-Similar Potentials and Quantum Algebras,ators realization it corresponds to the Darboux transformations technique for linear ODE of the second order. In this particular case the method was developed by Schrödinger and became well known to physicists due to the connections with quantum mechanics and supersymmetry. In the theory of orthogon

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Projection Operator Method for Quantum Groups,mathematics and mathematical physics in the end of the twentieth century. Although initially (in the early 1980’s) the quantum group theory was formulated for solving problems in the theory of integrable systems and statistical physics, later the surprising connection of this theory with many branch

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