From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Newsgroups: sci.math.num-analysis
Subject: Re: BOOK ON ASYMPTOTIC METHODS
Date: 16 Sep 1996 20:16:18 -0400

In article <51jafd$9k9@mo6.rc.tudelft.nl>,
D.P.Tran <D.P.Tran@et.tudelft.nl> wrote:
[ ... ]
>I LIKE TO LEARN ABOUT THE ASYMPTOTIC EXPANSIONS OF INTEGRALS VERY MUCH,
>BUT I DON’T KNOW WHERE TO START.
[ ... ]

 You can't go wrong with a classic:
 N.G. de Bruijn: Asymptotic methods in Analysis, 
 Dover Publications 1981, ISBN 0-486-64221-6
 (first printing 1958).

It covers: implicit functions, summation, Laplace method for integrals, 
the saddle point method and applications, and more.

Hope it helps, ZVK (Slavek).