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Hypergeometric Orthogonal Polynomials and Their q-Analogues

The very classical orthogonal polynomials named after Hermite, Laguerre and Jacobi, satisfy many common properties. For instance, they satisfy a second-order differential equation with polynomial coefficients and they can be expressed in terms of a hypergeometric function. Replacing the differential...

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Bibliographic Details
Main Authors: Koekoek, Roelof. (Author), Lesky, Peter A. (Author), Swarttouw, Ren ̌F. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
Series:Springer Monographs in Mathematics,
Subjects:
Mathematics.
Functions, special.
Special Functions.
Online Access:https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-05014-5
Table of Contents:
  • Foreword by Tom H. Koornwinder
  • Preface
  • 1.Definitions and miscellaneous formulas
  • 2.Polynomial solutions of eigenvalue problems
  • 3.Orthogonality of the polynomial solutions
  • Part I: Classical orthogonal polynomials
  • 4.Orthogonal polynomial solutions of differential equations, Continuous classical orthogonal polynomials
  • 5.Orthogonal polynomial solutions of real difference equations, Discrete classical orthogonal polynomials I
  • 6.Orthogonal polynomial solutions of complex difference equations, Discrete classical orthogonal polynomials II
  • 7.Orthogonal polynomial solutions in x(x+u) of real difference equations, Discrete classical orthogonal polynomials III
  • 8.Orthogonal polynomial solutions in z(z+u) of complex difference equations, Discrete classical orthogonal polynomials IV. Askey scheme of hypergeometric orthogonal polynomials
  • 9.Hypergeometric orthogonal polynomials
  • Part II: Classical q-orthogonal polynomials
  • 10.Orthogonal polynomial solutions of q-difference equation
  • Classical q-orthogonal polynomials I
  • 11.Orthogonal polynomial solutions in q-x of q-difference equations,Classical q-orthogonal polynomials II
  • 12.Orthogonal polynomial solutions in q-x +uqx of real q-difference equations, Classical q-orthogonal polynomials III
  • 13.Orthogonal polynomial solutions in a/z + uz/a of complex q-difference equations, Classical q-orthogonal polynomials IV
  • 14.Basic hypergeometric orthogonal polynomials
  • Bibliography
  • Index.

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