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Comments and reviews What are comments? It will focus on orthogonal polynomials and special functions, and feature lectures delivered by top researchers in their fields.
Orthogonal Polynomials and Special Functions
Namely: Krall or bispectral polynomials which, besides the orthogonality, are also common eigenfunctions of higher order differential or difference operators; and exceptional polynomials which have recently appeared in connection with quantum mechanic models associated to certain rational perturbations of the classical potentials.
We also explore the relationship between both extensions and how they can be used to expand Askey tableau.
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This will take us through the Sears and Watson transformations. We will also cover q-orthogonal polynomials and biorthogonal rational functions. As applications we will derive the Rogers-Ramanujan identities and some of their generalizations.
The study of the spectral properties of such operators leads to explicit information for the corresponding special functions. This approach will then be extended to other situations. We will give an introduction to elliptic hypergeometric series and integrals and discuss some relations to other topics such as solvable lattice models.