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Classical and quantum orthogonal polynomials in one variable [electronic resource] / Mourad E.H. Ismail ; with two chapters by Walter Van Assche.

By: Material type: TextTextSeries: Encyclopedia of mathematics and its applications ; v. 98.Publication details: Cambridge : Cambridge University Press, 2005.Description: 1 online resource (xviii, 706 p.) : illISBN:
  • 9781107089457 (electronic bk.)
  • 110708945X (electronic bk.)
Subject(s): Genre/Form: Additional physical formats: Print version:: Classical and quantum orthogonal polynomials in one variable.DDC classification:
  • 515.55 22
LOC classification:
  • QA404.5 .I85 2005eb
Other classification:
  • 31.24
  • 31.35
  • SK 230
Online resources:
Contents:
Preliminaries -- Orthogonal polynomials -- Differential equations -- Jacobi polynomials -- Some inverse problems -- Discrete orthogonal polynomials -- Zeros and inequalities -- Polynomials orthogonal on the unit circle -- Linearization, connections and integral representations -- The Sheffer classification -- q-series preliminaries -- q-summation theorems -- Some q-orthogonal polynomials -- Exponential and q-Bessel functions -- The Askey-Wilson polynomials -- The Askey-Wilson operators -- q-Hermite polynomials on the unit circle -- Discrete q-orthogonal polynomials -- Fractional and q-fractional calculus -- Polynomial solutions to functional equations -- Some indeterminate moment problems -- The Riemann-Hilbert problem -- Multiple orthogonal polynomials -- Research problems.
Review: "This is the first modern treatment of orthogonal polynomials from the viewpoint of special functions. The coverage is encyclopedic, including classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier, and Meixner polynomials, as well as those, e.g. Askey-Wilson and Al-Salam-Chihara, polynomial systems discovered over the last 50 years: multiple orthogonal polynomials are discussed for the first time in book form."--BOOK JACKET.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library EBSCO Mathematics Available
Total holds: 0

Includes bibliographical references and index.

Preliminaries -- Orthogonal polynomials -- Differential equations -- Jacobi polynomials -- Some inverse problems -- Discrete orthogonal polynomials -- Zeros and inequalities -- Polynomials orthogonal on the unit circle -- Linearization, connections and integral representations -- The Sheffer classification -- q-series preliminaries -- q-summation theorems -- Some q-orthogonal polynomials -- Exponential and q-Bessel functions -- The Askey-Wilson polynomials -- The Askey-Wilson operators -- q-Hermite polynomials on the unit circle -- Discrete q-orthogonal polynomials -- Fractional and q-fractional calculus -- Polynomial solutions to functional equations -- Some indeterminate moment problems -- The Riemann-Hilbert problem -- Multiple orthogonal polynomials -- Research problems.

"This is the first modern treatment of orthogonal polynomials from the viewpoint of special functions. The coverage is encyclopedic, including classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier, and Meixner polynomials, as well as those, e.g. Askey-Wilson and Al-Salam-Chihara, polynomial systems discovered over the last 50 years: multiple orthogonal polynomials are discussed for the first time in book form."--BOOK JACKET.

Description based on print version record.

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