Coverart for item
The Resource Classical and Quantum Orthogonal Polynomials in One Variable

Classical and Quantum Orthogonal Polynomials in One Variable

Label
Classical and Quantum Orthogonal Polynomials in One Variable
Title
Classical and Quantum Orthogonal Polynomials in One Variable
Creator
Subject
Genre
Language
eng
Summary
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback
Member of
Cataloging source
EBLCP
http://library.link/vocab/creatorName
Ismail, Mourad E. H
Dewey number
515.55
Index
index present
LC call number
QA404.5 .I85
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Encyclopedia of Mathematics and its Applications
Series volume
v. 98
http://library.link/vocab/subjectName
  • Orthogonal polynomials
  • MATHEMATICS
  • MATHEMATICS
  • Orthogonal polynomials
  • Orthogonale Polynome
  • Orthogonale reeksen
Label
Classical and Quantum Orthogonal Polynomials in One Variable
Instantiates
Publication
Note
12.4 Transformations
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover; Half Title; Series Page; Title; Copyright; Contents; Foreword; Preface; 1 Preliminaries; 1.1 Hermitian Matrices and Quadratic Forms; 1.2 Some Real and Complex Analysis; 1.3 Some Special Functions; 1.4 Summation Theorems and Transformations; Exercises; 2 Orthogonal Polynomials; 2.1 Construction of Orthogonal Polynomials; 2.2 Recurrence Relations; 2.3 Numerator Polynomials; 2.4 Quadrature Formulas; 2.5 The Spectral Theorem; 2.6 Continued Fractions; 2.7 Modifications of Measures: Christoffel and Uvarov; 2.8 Modifications of Measures: Toda; 2.9 Modification by Adding Finite Discrete Parts
  • 2.10 Modifications of Recursion Coefficients2.11 Dual Systems; Exercises; 3 Differential Equations Discriminants and Electrostatics; 3.1 Preliminaries; 3.2 Differential Equations; 3.3 Applications; 3.4 Discriminants; 3.5 An Electrostatic Equilibrium Problem; 3.6 Functions of the Second Kind; 3.7 Differential Relations and Lie Algebras; Exercises; 4 Jacobi Polynomials; 4.1 Orthogonality; 4.2 Differential and Recursion Formulas; 4.3 Generating Functions; 4.4 Functions of the Second Kind; 4.5 Ultraspherical Polynomials; 4.6 Laguerre and Hermite Polynomials; 4.7 Multilinear Generating Functions
  • 4.8 Asymptotics and Expansions4.9 Relative Extrema of Classical Polynomials; 4.10 The Bessel Polynomials; Exercises; 5 Some Inverse Problems; 5.1 Ultraspherical Polynomials; 5.2 Birth and Death Processes; 5.3 The Hadamard Integral; 5.4 Pollaczek Polynomials; 5.5 A Generalization; 5.6 Associated Laguerre and Hermite Polynomials; 5.7 Associated Jacobi Polynomials; 5.8 The J-Matrix Method; 5.9 The Meixner-Pollaczek Polynomials; Exercises; 6 Discrete Orthogonal Polynomials; 6.1 Meixner Polynomials; 6.2 Hahn, Dual Hahn, and Krawtchouk Polynomials; 6.3 Difference Equations
  • 6.4 Discrete Discriminants6.5 Lommel Polynomials; 6.6 An Inverse Operator; Exercises; 7 Zeros and Inequalities; 7.1 A Theorem of Markov; 7.2 Chain Sequences; 7.3 The Hellmann-Feynman Theorem; 7.4 Extreme Zeros of Orthogonal Polynomials; 7.5 Concluding Remarks; 8 Polynomials Orthogonal on the Unit Circle; 8.1 Elementary Properties; 8.2 Recurrence Relations; 8.3 Differential Equations; 8.4 Functional Equations and Zeros; 8.5 Limit Theorems; 8.6 Modifications of Measures; Exercises; 9 Linearization, Connections and Integral Representations; 9.1 Connection Coefficients
  • 9.2 The Ultraspherical Polynomials and Watson's Theorem9.3 Linearization and Power Series Coefficients; 9.4 Linearization of Products and Enumeration; 9.5 Representations for Jacobi Polynomials; 9.6 Addition and Product Formulas; 9.7 The Askey-Gasper Inequality; Exercises; 10 The Sheffer Classification; 10.1 Preliminaries; 10.2 Delta Operators; 10.3 Algebraic Theory; Exercises; 11 q-Series Preliminaries; 11.1 Introduction; 11.2 Orthogonal Polynomials; 11.3 The Bootstrap Method; 11.4 q-Differences; 12 q-Summation Theorems; 12.1 Basic Definitions; 12.2 Expansion Theorems; 12.3 Bilateral Series
Control code
850148944
Dimensions
unknown
Extent
1 online resource (728 pages)
Form of item
online
Isbn
9781107325982
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
(OCoLC)850148944
Label
Classical and Quantum Orthogonal Polynomials in One Variable
Publication
Note
12.4 Transformations
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Cover; Half Title; Series Page; Title; Copyright; Contents; Foreword; Preface; 1 Preliminaries; 1.1 Hermitian Matrices and Quadratic Forms; 1.2 Some Real and Complex Analysis; 1.3 Some Special Functions; 1.4 Summation Theorems and Transformations; Exercises; 2 Orthogonal Polynomials; 2.1 Construction of Orthogonal Polynomials; 2.2 Recurrence Relations; 2.3 Numerator Polynomials; 2.4 Quadrature Formulas; 2.5 The Spectral Theorem; 2.6 Continued Fractions; 2.7 Modifications of Measures: Christoffel and Uvarov; 2.8 Modifications of Measures: Toda; 2.9 Modification by Adding Finite Discrete Parts
  • 2.10 Modifications of Recursion Coefficients2.11 Dual Systems; Exercises; 3 Differential Equations Discriminants and Electrostatics; 3.1 Preliminaries; 3.2 Differential Equations; 3.3 Applications; 3.4 Discriminants; 3.5 An Electrostatic Equilibrium Problem; 3.6 Functions of the Second Kind; 3.7 Differential Relations and Lie Algebras; Exercises; 4 Jacobi Polynomials; 4.1 Orthogonality; 4.2 Differential and Recursion Formulas; 4.3 Generating Functions; 4.4 Functions of the Second Kind; 4.5 Ultraspherical Polynomials; 4.6 Laguerre and Hermite Polynomials; 4.7 Multilinear Generating Functions
  • 4.8 Asymptotics and Expansions4.9 Relative Extrema of Classical Polynomials; 4.10 The Bessel Polynomials; Exercises; 5 Some Inverse Problems; 5.1 Ultraspherical Polynomials; 5.2 Birth and Death Processes; 5.3 The Hadamard Integral; 5.4 Pollaczek Polynomials; 5.5 A Generalization; 5.6 Associated Laguerre and Hermite Polynomials; 5.7 Associated Jacobi Polynomials; 5.8 The J-Matrix Method; 5.9 The Meixner-Pollaczek Polynomials; Exercises; 6 Discrete Orthogonal Polynomials; 6.1 Meixner Polynomials; 6.2 Hahn, Dual Hahn, and Krawtchouk Polynomials; 6.3 Difference Equations
  • 6.4 Discrete Discriminants6.5 Lommel Polynomials; 6.6 An Inverse Operator; Exercises; 7 Zeros and Inequalities; 7.1 A Theorem of Markov; 7.2 Chain Sequences; 7.3 The Hellmann-Feynman Theorem; 7.4 Extreme Zeros of Orthogonal Polynomials; 7.5 Concluding Remarks; 8 Polynomials Orthogonal on the Unit Circle; 8.1 Elementary Properties; 8.2 Recurrence Relations; 8.3 Differential Equations; 8.4 Functional Equations and Zeros; 8.5 Limit Theorems; 8.6 Modifications of Measures; Exercises; 9 Linearization, Connections and Integral Representations; 9.1 Connection Coefficients
  • 9.2 The Ultraspherical Polynomials and Watson's Theorem9.3 Linearization and Power Series Coefficients; 9.4 Linearization of Products and Enumeration; 9.5 Representations for Jacobi Polynomials; 9.6 Addition and Product Formulas; 9.7 The Askey-Gasper Inequality; Exercises; 10 The Sheffer Classification; 10.1 Preliminaries; 10.2 Delta Operators; 10.3 Algebraic Theory; Exercises; 11 q-Series Preliminaries; 11.1 Introduction; 11.2 Orthogonal Polynomials; 11.3 The Bootstrap Method; 11.4 q-Differences; 12 q-Summation Theorems; 12.1 Basic Definitions; 12.2 Expansion Theorems; 12.3 Bilateral Series
Control code
850148944
Dimensions
unknown
Extent
1 online resource (728 pages)
Form of item
online
Isbn
9781107325982
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
(OCoLC)850148944

Library Locations

    • Thomas Jefferson LibraryBorrow it
      1 University Blvd, St. Louis, MO, 63121, US
      38.710138 -90.311107
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