The Resource Classical and Quantum Orthogonal Polynomials in One Variable
Classical and Quantum Orthogonal Polynomials in One Variable
Resource Information
The item Classical and Quantum Orthogonal Polynomials in One Variable represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Classical and Quantum Orthogonal Polynomials in One Variable represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.
This item is available to borrow from 1 library branch.
- Summary
- The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback
- Language
- eng
- Extent
- 1 online resource (728 pages)
- Note
- 12.4 Transformations
- 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
- Isbn
- 9781107325982
- Label
- Classical and Quantum Orthogonal Polynomials in One Variable
- Title
- Classical and Quantum Orthogonal Polynomials in One Variable
- Language
- eng
- Summary
- The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback
- 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
- 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
- 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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.umsl.edu/portal/Classical-and-Quantum-Orthogonal-Polynomials-in/uu7rlEtNzs4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.umsl.edu/portal/Classical-and-Quantum-Orthogonal-Polynomials-in/uu7rlEtNzs4/">Classical and Quantum Orthogonal Polynomials in One Variable</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.umsl.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.umsl.edu/">University of Missouri-St. Louis Libraries</a></span></span></span></span></div>
