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Anyone know a good reference for the asymptotic study of integrals of the form $\int_{\Gamma}f(s)e^{ng(s)}ds$ , $n\to\infty$, where $f(z)$ and $g(z)$ are analytic functions in the domain containing the contour $\Gamma$?. The books I have consulted only refer to the case where $g(z)$ has critical points and that study reduces to the method of Laplace or Waltson's lemma. But, i need to study the case where $g(z)$ has no critical points.

Thank you all for your help!

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"The books I have consulted" - it would be helpful to mention which books, so that we don't waste your time telling you to look at things you've already seen. – J. M. Nov 8 '11 at 23:21
@J.M:These are some of the books I read: "Asymptotic Analysis", "Complex Variables Introduction and Applications Second Edition" , "Applied Mathematics Science: Asymptotic Analysis and Techniques of Asymptotic Analysis", "The Theory of Functions by Titchmarsh" Thanks – Gardel Nov 8 '11 at 23:45
up vote 2 down vote accepted

"Applied Asymptotic Analysis" of Peter Miller ?

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Ok, I'll look to see if I can find. Thank you.. – Gardel Nov 9 '11 at 17:01

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