Integrating a Monster: Achieving a Solution with Elegance

[H_man]

\int_{0}^{\pi/2}(cos(\theta)*exp(-2[\pi(1-cos(\theta))]^2)/k^2)/erf(2\pi/k)

Where of course the error function erf is defined as:
<br /> erf(x)=2/\pi\int_{0}^{x}exp(-t^2)dt<br />

Anyway... this is the problem I want to integrate. I am not looking for someone to post a solution. My question is simply what is the best way of tackling this monster. My first thought is to expand each of the functions into a power series and use the "crank the handle" method. Not very elegant. Can anyone see a better/quicker method?

Thanks

Harry

 

[foxjwill]

<br /> \int_{0}^{\pi \over 2} cos(\theta) \frac{\exp\left ( \frac{-2\pi(1-cos\theta)^2}{k^2}\right ) }{erf(\frac{2\pi}{k})}d\theta<br />

Now, since erf doesn't depend on theta, you can take it out of the integral. After that, your best bet is to try series. It's possible you might be able to do this with contour integrals, although that might be equally as difficult, if even possible.

 

[H_man]

Cheers!