Classical and quantum orthogonal polynomials in one variable [E-Book] / Mourad E.H. Ismail ; with two chapters by Walter Van Assche.
Ismail, Mourad, (author)
Assche, Walter van, (author)
Cambridge : Cambridge University Press, 2005
1 online resource (xviii, 706 pages)
englisch
9780521143479
9781107325982
9780521782012
Encyclopedia of mathematics and its applications ; volume 98
Full Text
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.