Discrete Orthogonal Polynomials
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Discrete Orthogonal Polynomials
Author: J. Baik
language: en
Publisher: Princeton University Press
Release Date: 2007-01-02
This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
Encyclopedia of Special Functions: The Askey–Bateman Project
Author: Mourad E. H. Ismail
language: en
Publisher: Cambridge University Press
Release Date: 2020-09-17
Extensive update of the Bateman Manuscript Project. Volume 1 covers orthogonal polynomials and moment problems.
Classical Orthogonal Polynomials of a Discrete Variable
Author: Arnold F. Nikiforov
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
While classical orthogonal polynomials appear as solutions to hypergeometric differential equations, those of a discrete variable emerge as solutions of difference equations of hypergeometric type on lattices. The authors present a concise introduction to this theory, presenting at the same time methods of solving a large class of difference equations. They apply the theory to various problems in scientific computing, probability, queuing theory, coding and information compression. The book is an expanded and revised version of the first edition, published in Russian (Nauka 1985). Students and scientists will find a useful textbook in numerical analysis.