Consider the integral defined by

.

Use Laplace's method to obtain the first term of the asymptotic expansion of the integral as .

How can I start? Can someone point me to somewhere with a similar example?

Thank you.

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- Sep 22nd 2011, 07:21 AMmath2011Finding asymptotic expansion using Laplace's method
Consider the integral defined by

.

Use Laplace's method to obtain the first term of the asymptotic expansion of the integral as .

How can I start? Can someone point me to somewhere with a similar example?

Thank you. - Sep 23rd 2011, 12:06 AMCaptainBlackRe: Finding asymptotic expansion using Laplace's method
- Sep 25th 2011, 06:05 AMmath2011Re: Finding asymptotic expansion using Laplace's method
Thanks! I can see that the approximated solution is similar to the solution. But this question is definitely a Laplace method question. How can I apply the Laplace method to the question?

- Sep 25th 2011, 06:21 AMCaptainBlackRe: Finding asymptotic expansion using Laplace's method
Well that was the version of Laplace's method from the first part of this document, except the maximum is of is at an end point of the interval so not quadratic, and so this is covered by the middle paragraph of the further notes section.

CB - Sep 26th 2011, 07:58 AMmath2011Re: Finding asymptotic expansion using Laplace's method
According to the tutorial 2.8 referred to by the middle paragraph of the further notes section, the higher boundary should be taken to . This is what I got after doing that.

Thanks for helping me getting into this topic.