Asymptotics and Special Functions

by Frank Olver

Overview

A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.

Product Details

ISBN-13:	9781040187029
Publisher:	CRC Press
Publication date:	01/24/1997
Sold by:	Barnes & Noble
Format:	eBook
Pages:	592
File size:	4 MB

Table of Contents

Preface to A K Peters Edition, Preface, 1 Introduction to Asymptotic Analysis, 2 Introduction to Special Functions, 3 Integrals of a Real Variable, 4 Contour Integrals, 5 Differential Equations with Regular Singularities; Hypergeometric and Legendre Functions, 6 Tbe Liouville-Green Approximation, 7 Differential Equations with Irregular Singularities; Bessel and Confluent Hypergeometric Functions, 8 Sums and Sequences, 9 Integrals: Further Methods, 10 Differential Equations with a Parameter: Expansions in Elementary Functions, 11 Differential Equations with a Parameter: Turning Points, 12 Differential Equations with a Parameter: Simple Poles and Other Transition Points, 13 Connection Formulas for Solutions of Differential Equations, 14 Estimation of Remainder Terms, Answers to Exercises, References, Index of Symbols, General Index

What People are Saying About This

From the Publisher

The book under review is a very good reference on this material, giving a detailed collection of various asymptotic results, with a special focus on special functions. … The book is a classic, and it seems to be essentially a research text, but it has the structure to be also used as a textbook. Indeed, each section includes good and challenging exercises, some of which are the key and starting point for further research. … This impressive book contains more than what appears in its table of contents; the reader will find much that is very nice and useful inside it. I recommend it strongly for students and professors of mathematics, physics and engineering who are concerned with careful analysis of asymptotics and special functions.
—MAA Reviews, July 2011

Editorial Reviews

A two-semester graduate textbook providing a comprehensive introduction to two topics of classical analysis. Presumes a good grounding in advanced calculus and complex-variable theory; previous knowledge of ordinary differential equations would be helpful but not essential. Includes error bounds or methods for obtaining them for most of the approximations and expansions. Reissued with corrections from the 1974 edition published by Academic Press. Annotation c. by Book News, Inc., Portland, Or.

Booknews

The book under review is a very good reference on this material, giving a detailed collection of various asymptotic results, with a special focus on special functions. … The book is a classic, and it seems to be essentially a research text, but it has the structure to be also used as a textbook. Indeed, each section includes good and challenging exercises, some of which are the key and starting point for further research. … This impressive book contains more than what appears in its table of contents; the reader will find much that is very nice and useful inside it. I recommend it strongly for students and professors of mathematics, physics and engineering who are concerned with careful analysis of asymptotics and special functions.
—MAA Reviews, July 2011

From the Publisher