This is the first of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 1 contains most of the material on orthogonal polynomials, from the classical orthogonal polynomials of Hermite, Laguerre and Jacobi to the Askey–Wilson polynomials, which are the most general basic hypergeometric orthogonal polynomials. Separate chapters cover orthogonal polynomials on the unit circle, zeros of orthogonal polynomials and matrix orthogonal polynomials, with detailed results about matrix-valued Jacobi polynomials. A chapter on moment problems provides many examples of indeterminate moment problems. A thorough bibliography rounds off what will be an essential reference.
1. Preliminaries Mourad E. H. Ismail; 2. General orthogonal polynomials Mourad E. H. Ismail; 3. Jacobi and related polynomials Mourad E. H. Ismail; 4. Recursively defined polynomials Mourad E. H. Ismail; 5. Wilson and related polynomials Mourad E. H. Ismail; 6. Discrete orthogonal polynomials Mourad E. H. Ismail; 7. Some q-orthogonal polynomials Mourad E. H. Ismail; 8. The Askey–Wilson family of polynomials Mourad E. H. Ismail; 9. Orthogonal polynomials on the unit circle Leonid Golinskii; 10. Zeros of orthogonal polynomials Andrea Laforgia and Martin E. Muldoon; 11. The moment problem Christian Berg and Jacob S. Christiansen; 12. Matrix valued orthogonal polynomials and differential equations Antonio J. Durán and F. Alberto Grünbaum; 13. Some families of matrix valued Jacobi orthogonal polynomials F. Alberto Grünbaum, I. Pacharoni and J. A. Tirao; References; Index.
Mourad E. H. Ismail is Research Professor at the University of Central Florida.
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