Serving both as an introduction to the subject and as a reference,
this book presents the theory in elegant form and with modern
concepts and notation. It covers the general theory and emphasizes
the classical types of orthogonal polynomials whose weight
functions are supported on standard domains. The approach is a
blend of classical analysis and symmetry group theoretic methods.
Finite reflection groups are used to motivate and classify
symmetries of weight functions and the associated polynomials. This
revised edition has been updated throughout to reflect recent
developments in the field. It contains 25% new material, including
two brand new chapters on orthogonal polynomials in two variables,
which will be especially useful for applications, and orthogonal
polynomials on the unit sphere. The most modern and complete
treatment of the subject available, it will be useful to a wide
audience of mathematicians and applied scientists, including
physicists, chemists and engineers.
General
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