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