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.
Fractional integration and fractional differentiation for $d$-dimensional Jacobi expansions by C. Balderrama and W. O. Urbina R. Sutherland-type trigonometric models, trigonometric invariants, and multivariate polynomials by K. G. Boreskov, A. V. Turbiner, and J. C. Lopez Vieyra Polynomials associated with partitions: Asymptotics and zeros by R. P. Boyer and W. M. Y. Goh A generating function for the $N$-soliton solutions of the Kadomtsev-Petviashvili II equation by S. Chakravarty and Y. Kodama Asymptotics of the second Painleve equation by P. A. Clarkson Evaluation of certain Mellin transformations in terms of the trigamma and polygamma functions by M. W. Coffey Conformal maps to generalized quadrature domains by D. Crowdy and J. Marshall Approximations for zeros of Hermite functions by A Elbert and M. E. Muldoon Inequalities and bounds for elliptic integrals II by H. Kazi and E. Neuman P-symbols, Heun identities, and $ 3F 2$ identities by R. S. Maier An iterative method for numerical integration of rational functions by D. Manna and V. H. Moll A Taylor expansion theorem for an elliptic extension of the Askey-Wilson operator by M. J. Schlosser Ramanujan's symmetric theta functions in his lost notebook by S. H. Son Integral representations for products of Airy functions and their fractional derivatives by V. Varlamov.