**Contemporary Mathematics**

Volume: 471;
2008;
218 pp;
Softcover

MSC: Primary 33;

Print ISBN: 978-0-8218-4650-6

Product Code: CONM/471

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-8150-7
Product Code: CONM/471.E**

List Price: $75.00

Individual Member Price: $60.00

# Special Functions and Orthogonal Polynomials

Share this page *Edited by *
*Diego Dominici; Robert S. Maier*

This volume contains fourteen articles that represent the AMS Special
Session on Special Functions and Orthogonal Polynomials, held in
Tucson, Arizona in April of 2007. It gives an overview of the modern
field of special functions with all major subfields represented,
including: applications to algebraic geometry, asymptotic analysis,
conformal mapping, differential equations, elliptic functions,
fractional calculus, hypergeometric and \(q\)-hypergeometric
series, nonlinear waves, number theory, symbolic and numerical
evaluation of integrals, and theta functions. A few articles are
expository, with extensive bibliographies, but all contain original
research.

This book is intended for pure and applied mathematicians who are interested
in recent developments in the theory of special functions. It covers a wide
range of active areas of research and demonstrates the vitality of the
field.

#### Table of Contents

# Table of Contents

## Special Functions and Orthogonal Polynomials

- Contents iii4 free
- Preface v6 free
- Fractional integration and fractional differentiation for d-dimensional Jacobi expansions 18 free
- Sutherland-type trigonometric models, trigonometric invariants, and multivariate polynomials 1522
- Polynomials associated with partitions: Asymptotics and zeros 3340
- A generating function for the N-soliton solutions of the Kadomtsev–Petviashvili II equation 4754
- Asymptotics of the second Painlevé equation 6976
- Evaluation of certain Mellin transformations in terms of the trigamma and polygamma functions 8592
- Conformal maps to generalized quadrature domains 105112
- Approximations for zeros of Hermite functions 117124
- Inequalities and bounds for elliptic integrals II 127134
- P-symbols, Heun identities, and 3F2 identities 139146
- An iterative method for numerical integration of rational functions 161168
- A Taylor expansion theorem for an elliptic extension of the Askey–Wilson operator 175182
- Ramanujan's symmetric theta functions in his Lost Notebook 187194
- Integral representations for products of Airy functions and their fractional derivatives 203210

#### Readership

Graduate students and research mathematicians interested in orthogonal polynomials and special functions.