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Basic hypergeometric orthogonal polynomials

Basic hypergeometric orthogonal polynomials

Date: 2016..02..16
Event: CARMA
Venue: University of New Castle. Australia

Abstract

We will review the (now classical) scheme of basic (\(q\)-)hypergeometric orthogonal polynomials. It contains more than twenty families; for each family there exists at least one positive weight with respect to which the polynomials are orthogonal provided the parameter \(q\) is real and lies between 0 and 1. In the talk we will describe how to reduce the scheme allowing the parameters in the families to be complex. The construction leads to new orthogonality properties or to generalization of known ones to the complex plane.

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