Classical and quantum orthogonal polynomials in one variable

The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback. Its encyclopedic coverage includes classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier and Meixner polynomials as well as those discovered over the last 50 years...

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Main Authors: Ismail, Mourad, Assche, Walter van (Author)
Format: eBook
Language:English
Published: Cambridge Cambridge University Press 2005
Series:Encyclopedia of mathematics and its applications
Subjects:
Online Access:
Collection: Cambridge Books Online - Collection details see MPG.ReNa
Table of 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