Answer by doraemonpaul for Doing Some Asymptotic Integration: Problem with a...
Following the approach like Difficult Gaussian Integral Involving Two Trig Functions in the Exponent: Any Help?, you will get the two key types of integral:...
View ArticleAnswer by Math.StackExchange for Doing Some Asymptotic Integration: Problem...
When you substitute the very last arctan with arcsin, you should remember:$\sin^2(\arcsin(a/b))=(\sin(\arcsin(a/b)))^2=(a/b)^2$ So, $a/0$ appears as the following:$\frac{b...
View ArticleDoing Some Asymptotic Integration: Problem with a Taylor Series
I evaluated this integral (with some help from you guys):$$\int_0^{\arcsin\left(\frac{a}{b}\right)} \exp\left(-\beta\left(b\cos(x)-\sqrt{a^2 - b^2 \sin^2(x)}\right)^2 \right) \, dx$$and got an answer...
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