Classical and Quantum Orthogonal Polynomials in One Variable

Mourad E. H. Ismail is Professor of Mathematics at the University of Central Florida.

• Foreword; Preface; 1. Preliminaries; 2. Orthogonal polynomials; 3. Differential equations, Discriminants and electrostatics; 4. Jacobi polynomials; 5. Some inverse problems; 6. Discrete orthogonal polynomials; 7. Zeros and inequalities; 8. Polynomials orthogonal on the unit circle; 9. Linearization, connections and integral representations; 10. The Sheffer classification; 11. q-series Preliminaries; 12. q-Summation theorems; 13. Some q-Orthogonal polynomials; 14. Exponential and q-bessel functions; 15. The Askey-Wilson polynomials; 16. The Askey-Wilson operators; 17. q-Hermite polynomials on the unit circle; 18. Discrete q-orthogonal polynomials; 19. Fractional and q-fractional calculus; 20. Polynomial solutions to functional equations; 21. Some indeterminate moment problems; 22. The Riemann-Hilbert problem for orthogonal polynomials; 23. Multiple orthogonal polynomials; 24. Research problems; Bibliography; Index; Author index.

'… an ambitious and imposing testament to the author's eminence in and love for the subject. All research workers in orthogonal polynomials will want to own this special work. I feel fortunate to have a copy of it.' The Mathematical Intelligencer