Asymptotics and Special Functions

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

• 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