The Resource Hypergeometric orthogonal polynomials and their q-analogues, Roelof Koekoek, Peter A. Lesky, René F. Swarttouw ; with a foreword by Tom H. Koornwinder

Hypergeometric orthogonal polynomials and their q-analogues, Roelof Koekoek, Peter A. Lesky, René F. Swarttouw ; with a foreword by Tom H. Koornwinder

Label
Hypergeometric orthogonal polynomials and their q-analogues
Title
Hypergeometric orthogonal polynomials and their q-analogues
Statement of responsibility
Roelof Koekoek, Peter A. Lesky, René F. Swarttouw ; with a foreword by Tom H. Koornwinder
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
UKM
Dewey number
515.55
Index
index present
LC call number
QA404.5
LC item number
.K64 2010
Literary form
non fiction
Nature of contents
bibliography
Series statement
Springer monographs in mathematics,
Label
Hypergeometric orthogonal polynomials and their q-analogues, Roelof Koekoek, Peter A. Lesky, René F. Swarttouw ; with a foreword by Tom H. Koornwinder
Publication
Bibliography note
Includes bibliographical references and index
http://library.link/vocab/branchCode
  • net
Contents
  • Contents note continued: 10.1.Polynomial Solutions of q-Difference Equations -- 10.2.The Basic Hypergeometric Representation -- 10.3.The Three-Term Recurrence Relation -- 10.4.Classification of the Positive-Definite Orthogonal Polynomial Solutions -- 10.5.Solutions of the q-Pearson Equation -- 10.6.Orthogonality Relations -- 11.Orthogonal Polynomial Solutions in q-x of q-Difference Equations -- Classical q-Orthogonal Polynomials II -- 11.1.Polynomial Solutions in q-x of q-Difference Equations -- 11.2.The Basic Hypergeometric Representation -- 11.3.The Three-Term Recurrence Relation -- 11.4.Orthogonality and the Self-Adjoint Operator Equation -- 11.5.Rodrigues Formulas -- 11.6.Classification of the Positive-Definite Orthogonal Polynomial Solutions -- 11.7.Solutions of the q-1-Pearson Equation -- 11.8.Orthogonality Relations -- 12.Orthogonal Polynomial Solutions in q-x+uqx of Real q-Difference Equations -- Classical q-Orthogonal Polynomials III --
  • Contents note continued: 12.1.Motivation for Polynomials in q-x+uqx Through Duality -- 12.2.Difference Equations Having Real Polynomial Solutions with Argument q-x + uqx -- 12.3.The Basic Hypergeometric Representation -- 12.4.The Three-Term Recurrence Relation -- 12.5.Classification of the Positive-Definite Orthogonal Polynomial Solutions -- 12.6.Solutions of the q-Pearson Equation -- 12.7.Orthogonality Relations -- 13.Orthogonal Polynomial Solutions in a/z+uz/a of Complex q-Difference Equations -- Classical q-Orthogonal Polynomials IV -- 13.1.Real Polynomial Solutions in a/z+uz/a with u f R \{0} and a, z f C\{0} -- 13.2.Classification of the Positive-Definite Orthogonal Polynomial Solutions -- 13.3.Solutions of the q-Pearson Equation -- 13.4.Orthogonality Relations -- Scheme of Basic Hypergeometric Orthogonal Polynomials -- 14.Basic Hypergeometric Orthogonal Polynomials -- 14.1.Askey-Wilson -- 14.2.q-Racah -- 14.3.Continuous Dual q-Hahn -- 14.4.Continuous q-Hahn --
  • Contents note continued: 14.5.Big q-Jacobi -- 14.5.1.Big q-Legendre -- 14.6.q-Hahn -- 14.7.Dual q-Hahn -- 14.8.Al-Salam-Chihara -- 14.9.q-Meixner-Pollaczek -- 14.10.Continuous q-Jacobi -- 14.10.1.Continuous q-Ultraspherical/Rogers -- 14.10.2.Continuous q-Legendre -- 14.11.Big q-Laguerre -- 14.12.Little q-Jacobi -- 14.12.1.Little q-Legendre -- 14.13.q-Meixner -- 14.14.Quantum q-Krawtchouk -- 14.15.q-Krawtchouk -- 14.16.Affine q-Krawtchouk -- 14.17.Dual q-Krawtchouk -- 14.18.Continuous Big q-Hermite -- 14.19.Continuous q-Laguerre -- 14.20.Little q-Laguerre/Wall -- 14.21.q-Laguerre -- 14.22.q-Bessel -- 14.23.q-Charlier -- 14.24.Al-Salam-Carlitz I -- 14.25.Al-Salam-Carlitz II -- 14.26.Continuous q-Hermite -- 14.27.Stieltjes-Wigert -- 14.28.Discrete q-Hermite I -- 14.29.Discrete q-Hermite II
  • Contents note continued: 2.5.Existence of a Three-Term Recurrence Relation -- 2.6.Explicit Form of the Three-Term Recurrence Relation -- 3.Orthogonality of the Polynomial Solutions -- 3.1.Favard's Theorem -- 3.2.Orthogonality and the Self-Adjoint Operator Equation -- 3.3.The Jackson-Thomae q-Integral -- 3.4.Rodrigues Formulas -- 3.5.Duality -- pt. I Classical Orthogonal Polynomials -- 4.Orthogonal Polynomial Solutions of Differential Equations -- Continuous Classical Orthogonal Polynomials -- 4.1.Polynomial Solutions of Differential Equations -- 4.2.Classification of the Positive-Definite Orthogonal Polynomial Solutions -- 4.3.Properties of the Positive-Definite Orthogonal Polynomial Solutions -- 5.Orthogonal Polynomial Solutions of Real Difference Equations -- Discrete Classical Orthogonal Polynomials I -- 5.1.Polynomial Solutions of Real Difference Equations -- 5.2.Classification of the Positive-Definite Orthogonal Polynomial Solutions --
  • Contents note continued: 5.3.Properties of the Positive-Definite Orthogonal Polynomial Solutions -- 6.Orthogonal Polynomial Solutions of Complex Difference Equations -- Discrete Classical Orthogonal Polynomial II -- 6.1.Real Polynomial Solutions of Complex Difference Equations -- 6.2.Classification of the Real Positive-Definite Orthogonal Polynomial Solutions -- 6.3.Properties of the Positive-Definite Orthogonal Polynomial Solutions -- 7.Orthogonal Polynomial Solutions in x(x+u) of Real Difference Equations -- Discrete Classical Orthogonal Polynomials III -- 7.1.Motivation for Polynomials in x(x+u) Through Duality -- 7.2.Difference Equations Having Real Polynomial Solutions with Argument x(x+u) -- 7.3.The Hypergeometric Representation -- 7.4.The Three-Term Recurrence Relation -- 7.5.Classification of the Positive-Definite Orthogonal Polynomial Solutions -- 7.6.The Self-Adjoint Difference Equation -- 7.7.Orthogonality Relations for Dual Hahn Polynomials --
  • Contents note continued: 7.8.Orthogonality Relations for Racah Polynomials -- 8.Orthogonal Polynomial Solutions in z(z+u) of Complex Difference Equations -- Discrete Classical Orthogonal Polynomials IV -- 8.1.Real Polynomial Solutions of Complex Difference Equations -- 8.2.Orthogonality Relations for Continuous Dual Hahn Polynomials -- 8.3.Orthogonality Relations for Wilson Polynomials -- Askey Scheme of Hypergeometric Orthogonal Polynomials -- 9.Hypergeometric Orthogonal Polynomials -- 9.1.Wilson -- 9.2.Racah -- 9.3.Continuous Dual Hahn -- 9.4.Continuous Hahn -- 9.5.Hahn -- 9.6.Dual Hahn -- 9.7.Meixner-Pollaczek -- 9.8.Jacobi -- 9.8.1.Gegenbauer/Ultraspherical -- 9.8.2.Chebyshev -- 9.8.3.Legendre/Spherical -- 9.9.Pseudo Jacobi -- 9.10.Meixner -- 9.11.Krawtchouk -- 9.12.Laguerre -- 9.13.Bessel -- 9.14.Charlier -- 9.15.Hermite -- pt. II Classical q-Orthogonal Polynomials -- 10.Orthogonal Polynomial Solutions of q-Difference Equations -- Classical q-Orthogonal Polynomials I --
  • Machine generated contents note: 1.Definitions and Miscellaneous Formulas -- 1.1.Orthogonal Polynomials -- 1.2.The Gamma and Beta Function -- 1.3.The Shifted Factorial and Binomial Coefficients -- 1.4.Hypergeometric Functions -- 1.5.The Binomial Theorem and Other Summation Formulas -- 1.6.Some Integrals -- 1.7.Transformation Formulas -- 1.8.The q-Shifted Factorial -- 1.9.The q-Gamma Function and q-Binomial Coefficients -- 1.10.Basic Hypergeometric Functions -- 1.11.The q-Binomial Theorem and Other Summation Formulas -- 1.12.More Integrals -- 1.13.Transformation Formulas -- 1.14.Some q-Analogues of Special Functions -- 1.15.The q-Derivative and q-Integral -- 1.16.Shift Operators and Rodrigues-Type Formulas -- 2.Polynomial Solutions of Eigenvalue Problems -- 2.1.Hahn's q-Operator -- 2.2.Eigenvalue Problems -- 2.3.The Regularity Condition -- 2.4.Determination of the Polynomial Solutions -- 2.4.1.First Approach -- 2.4.2.Second Approach --
Control code
000045959436
Dimensions
25 cm
Extent
xix, 578 p.
Isbn
9783642050138
Lccn
2010923797
http://library.link/vocab/recordID
.b27159759
System control number
  • (OCoLC)449851721
  • springer3642050131

Library Locations

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      -38.195656 144.304955
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