3 edition of Classical and quantum orthogonal polynomials in one variable found in the catalog.
Classical and quantum orthogonal polynomials in one variable
Includes bibliographical references (p. 663-698) and index.
|Statement||Mourad E.H. Ismail ; with two chapters by Walter Van Assche.|
|Series||Encyclopedia of mathematics and its applications -- v. 98|
|Contributions||Assche, Walter van, 1958-|
|LC Classifications||QA404.5 .I85 2009|
|The Physical Object|
|Pagination||xviii, 708 p. :|
|Number of Pages||708|
|LC Control Number||2010286005|
Preliminaries; 2. Differential equations, Discriminants and electrostatics; 4. They include many orthogonal polynomials as special cases, such as the Meixner—Pollaczek polynomialsthe continuous Hahn polynomialsthe continuous dual Hahn polynomialsand the classical polynomials, described by the Askey scheme The Askey—Wilson polynomials introduce an extra parameter q into the Wilson polynomials. Properties[ edit ] Orthogonal polynomials of one variable defined by a non-negative measure on the real line have the following properties. Examples of orthogonal polynomials in several variables; 6. The Askey—Wilson polynomials are the special case of Macdonald polynomials for a certain non-reduced root system of rank 1.
Sometimes the measure has finite support, in which case the family of orthogonal polynomials is finite, rather than an infinite sequence. The book, which is intended both as an introduction to the subject and as a reference, presents the theory in elegant form and with modern concepts and notation. Another feature is that the presentation is simplified, avoiding several constants that previously guaranteed orthonormality. Such a W is called a weight function. Simplicity, clarity of exposition, thoughtfully designed exercises are among the book's strengths. Those who are familiar with the fist edition will recognize of course its content, but they should be pointed to the two new chapters 2 and 3, and a considerable update of chapter 5 with explicit examples of orthogonal polynomials in several variables.
Such a W is called a weight function. Orthogonal polynomials associated with symmetric groups; One can also consider orthogonal polynomials for some curve in the complex plane. Berndt, Mathematical Reviews " See also. Applications can be found in quantum mechanics.
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Also most of the chapters have a section with exercises, which range from being easy to having to look up research papers in order to be able to solve them.
Most of Ismail's work is joint with other mathematicians and physicists and some of his papers are interdisciplinary. Orthogonal polynomials associated with octahedral groups, and applications: This is the symmetric group but now including additionally signs, giving the symmetry groups for hypercubes and hyperoctahedra.
They can sometimes be written in terms of Jacobi polynomials. Another feature is that the presentation is simplified, avoiding several constants that previously guaranteed orthonormality. Askey-Wilson and Al-Salam--Chihara polynomial systems discovered over the last 50 years and multiple orthogonal polynomials are discussed for the first time in book form.
For the history and more extensive technical details, the reader is guided to the literature. He is among the ISI highly cited scientists.
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Sieved orthogonal polynomials, such as the sieved ultraspherical polynomials, sieved Jacobi polynomials, and sieved Pollaczek polynomials, have modified recurrence relations.
Generalized classical orthogonal polynomials: With this chapter, one is even more on familiar ground. Reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. General properties of orthogonal polynomials in several variables: This generalizes the classical theory in one variable: moment problem, matrix form of the three-term recurrence relation, reproducing kernels, Fourier series, location of the zeros, and Gaussian cubature.
Preliminaries; 2. Examples of orthogonal polynomials The most commonly used orthogonal polynomials are orthogonal for a measure with support in a real interval. He published over research articles, one book and edited several books.
He worked on infinite divisibility problems in probability that led to questions about monotonicity properties of special functions. Research problems; Bibliography; Index; Author index. It introduces all the necessary material, and it follows the main flow of the ideas, with further technical and historical details banned to the end-notes for each chapter that forward the reader to the necessary literature.
Recurrent relation The polynomials Pn satisfy a recurrent relation of the form See Favard's theorem for a converse result. Ismail is also interested in the combinatorial theory of orthogonal polynomials and their linearization coefficients.
Examples of orthogonal polynomials The most commonly used orthogonal polynomials are orthogonal for a measure with support in a real interval. Discrete orthogonal polynomials are orthogonal with respect to some discrete measure.
Download eBook This volume contains the proceedings of a conference held at the Courant Institute in to celebrate the 60th birthday of Percy A. Background: Introduction to hypergeometric series and classical orthogonal polynomials in one variable. Also the applications are mentioned where possible.Buy Classical and Quantum Orthogonal Polynomials in One Variable (Encyclopedia of Mathematics and its Applications) 1 by Mourad E.
H. Ismail (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible hildebrandsguld.com: Mourad E. H. Ismail. ORTHOGONAL POLYNOMIALS IN ONE OR MORE VARIABLES If Ais a measurable subset of Rn, two functions f;g: A!R are said to be orthogonal with respect to a weight function w: A!R if R A fgwdm= 0 where mis the usual measure on Rn.
A familiar example is the theory of Fourier series which is based on the fact any two functions in. hildebrandsguld.com: Classical and Quantum Orthogonal Polynomials in One Variable (Encyclopedia of Mathematics and its Applications) () by Ismail, Mourad E.
and a great selection of similar New, Used and Collectible Books available now at great hildebrandsguld.com Range: $ - $ Orthogonalpolynomials,ashortintroduction hildebrandsguld.cominder Abstract This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes.
It ends with some remarks about the usage of computer algebra for this theory. The paper will appear as a chapter in the book “Computer Algebra in QuantumCited by: 2. Titre: Classical and Quantum Orthogonal Polynomials in One Variable, Volume 13 Classical and quantum orthogonal polynomials in one variable, Walter van Assche Numéro 98 de Encyclopedia of Mathematics and its Applications, ISSN Auteurs5/5(2).
Zeros. If the measure dα is supported on an interval [a, b], all the zeros of P n lie in [a, b].Moreover, the zeros have the following interlacing property: if m>n, there is a zero of P m between any two zeros of P n. Multivariate orthogonal polynomials. The Macdonald polynomials are orthogonal polynomials in several variables, depending on the choice of an affine root system.