SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #16  -------------   OP-SF NET 8.6  -------------  November 15, 2001
From: OP-SF NET Editor (
Subject: Selected Papers of Frank Olver

World Scientific Series in 20th Century Mathematics - Vol. 7

(In 2 Volumes)

edited by Roderick Wong (City University of Hong Kong)
Pub. date: Jan 2000
ISBN 981-02-4106-2(set)
US$236 / 161

This is a collection of selected papers written by Frank W J Olver from 1949
to 1999. It contains his most important contributions to the fields of
asymptotic analysis and numerical analysis, including the global existence
of uniform asymptotic expansions for solution of ordinary differential
equations and construction of error bounds. It is a valuable collection for
anyone who works in, or uses, asymptotics, and should be on the shelves of
all major libraries.

   - The Asymptotic Solution of Linear Differential Equations of the Second
       Order for Large Values of a Parameter
   -  The Asymptotic Expansion of Bessel Functions of Large Order Uniform
       Asymptotic Expansions for Weber Parabolic Cylinder Functions of
       Large Orders
   -  Error Bounds for the Liouville-Green (or WKB) Approximation
   -  Error Analysis of Phase-Integral Methods
   -  Numerical Solution of Second-Order Linear Difference Equations
   -  Unsolved Problems in the Asymptotic Estimation of Special Functions
   -  General Connection Formulae for Liouville-Green Approximations in the
        Complex Plane
   -  Beyond Floating Point
   -  On Stokes' Phenomenon and Converging Factors
   -  Airy and Bessel Functions by Parallel Integration of ODEs
   -  Hyperasymptotic Solutions of Second-Order Linear Differential Equations
   -  On the Asymptotic and Numerical Solution of Linear Ordinary Differential
     and 42 other papers

Readership: Graduates in asymptotic analysis, differential equations and
numerical & computational methods.

"These two volumes exemplify a redoubtable mathematical talent, the work of
a man who has done more than almost anyone else in the 20th century to
bestow on the discipline of applied mathematics the elegance and rigor that
its earliest practitioners such as Gauss and Laplace would have wished for
it ... the books are beautifully bound and printed ... D S Jones has
contributed an intimate and adulatory introduction, and Roderick Wong should
be congratulated for bringing the entire effort to fruition."
(From the review by Jet Wimp in SIAM Review, Vol 43, 2001)

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