The lectures fall into two categories: on one hand we have lectures on computational
aspects of orthogonal polynomials and special functions and on the
other hand we have some modern applications. The computational aspects
deal with algorithms for computing quantities related to orthogonal polynomials
and quadrature (Walter Gautschi’s contribution), but recently it was
also found that computational aspects of numerical linear algebra are closely
related to the asymptotic behavior of (discrete) orthogonal polynomials. The
contributions of Andrei Mart´ınez and Bernhard Beckermann deal with this interaction
between numerical linear algebra, logarithmic potential theory and
asymptotics of discrete orthogonal polynomials. The contribution of Adhemar
Bultheel makes the transition between applications (linear prediction of
discrete stationary time series) and computational aspects of orthogonal rational
functions on the unit circle and their matrix analogues. Other applications
in this volume are quantum integrability and separation of variables (Vadim
Kuznetsov), the classification of orthogonal polynomials in terms of two linear
transformations each tridiagonal with respect to an eigenbasis of the other
(Paul Terwilliger), and the theory of nonlinear special functions arising from
the Painlev´e equations (Peter Clarkson)