Electronic ISBN:  9780821881507 
Product Code:  CONM/471.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $60.00 

Book DetailsContemporary MathematicsVolume: 471; 2008; 218 ppMSC: Primary 33;
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.ReadershipGraduate students and research mathematicians interested in orthogonal polynomials and special functions.

Table of Contents

Articles

Cristina Balderrama and Wilfredo O. Urbina R.  Fractional integration and fractional differentiation for $d$dimensional Jacobi expansions [ MR 2367408 ]

K. G. Boreskov, A. V. Turbiner and J. C. López Vieyra  Sutherlandtype trigonometric models, trigonometric invariants, and multivariate polynomials [ MR 2367409 ]

Robert P. Boyer and William M. Y. Goh  Polynomials associated with partitions: asymptotics and zeros [ MR 2367410 ]

Sarbarish Chakravarty and Yuji Kodama  A generating function for the $N$soliton solutions of the KadomtsevPetviashvili II equation [ MR 2367411 ]

Peter A. Clarkson  Asymptotics of the second Painlevé equation [ MR 2367412 ]

Mark W. Coffey  Evaluation of certain Mellin transformations in terms of the trigamma and polygamma functions [ MR 2367413 ]

Darren Crowdy and Jonathan Marshall  Conformal maps to generalized quadrature domains [ MR 2367414 ]

Árpád Elbert and Martin E. Muldoon  Approximations for zeros of Hermite functions [ MR 2367415 ]

Haseeb Kazi and Edward Neuman  Inequalities and bounds for elliptic integrals. II [ MR 2367416 ]

Robert S. Maier  $P$symbols, Heun identities, and ${}_3F_2$ identities [ MR 2367417 ]

Dante Manna and Victor H. Moll  An iterative method for numerical integration of rational functions [ MR 2367419 ]

Michael J. Schlosser  A Taylor expansion theorem for an elliptic extension of the AskeyWilson operator [ MR 2367418 ]

Seung H. Son  Ramanujan’s symmetric theta functions in his lost notebook [ MR 2367420 ]

Vladimir Varlamov  Integral representations for products of Airy functions and their fractional derivatives [ MR 2367421 ]


Additional Material

RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
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.
Graduate students and research mathematicians interested in orthogonal polynomials and special functions.

Articles

Cristina Balderrama and Wilfredo O. Urbina R.  Fractional integration and fractional differentiation for $d$dimensional Jacobi expansions [ MR 2367408 ]

K. G. Boreskov, A. V. Turbiner and J. C. López Vieyra  Sutherlandtype trigonometric models, trigonometric invariants, and multivariate polynomials [ MR 2367409 ]

Robert P. Boyer and William M. Y. Goh  Polynomials associated with partitions: asymptotics and zeros [ MR 2367410 ]

Sarbarish Chakravarty and Yuji Kodama  A generating function for the $N$soliton solutions of the KadomtsevPetviashvili II equation [ MR 2367411 ]

Peter A. Clarkson  Asymptotics of the second Painlevé equation [ MR 2367412 ]

Mark W. Coffey  Evaluation of certain Mellin transformations in terms of the trigamma and polygamma functions [ MR 2367413 ]

Darren Crowdy and Jonathan Marshall  Conformal maps to generalized quadrature domains [ MR 2367414 ]

Árpád Elbert and Martin E. Muldoon  Approximations for zeros of Hermite functions [ MR 2367415 ]

Haseeb Kazi and Edward Neuman  Inequalities and bounds for elliptic integrals. II [ MR 2367416 ]

Robert S. Maier  $P$symbols, Heun identities, and ${}_3F_2$ identities [ MR 2367417 ]

Dante Manna and Victor H. Moll  An iterative method for numerical integration of rational functions [ MR 2367419 ]

Michael J. Schlosser  A Taylor expansion theorem for an elliptic extension of the AskeyWilson operator [ MR 2367418 ]

Seung H. Son  Ramanujan’s symmetric theta functions in his lost notebook [ MR 2367420 ]

Vladimir Varlamov  Integral representations for products of Airy functions and their fractional derivatives [ MR 2367421 ]