Finally …

Posted by tpc at November 28th, 2004

Finally my maths blog is up and running, all thanks to that web-savvy someone.

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Irritating Integral

Posted by tpc at November 28th, 2004

It took me almost a week to prove \int_0^{\pi} \log (1+4\cos^2(u)) du = 2\pi \log{\phi} where \phi = (\sqrt{5}+1)/2.

A time consuming but fruitful exercise. I had tried all the integration tricks I know, resorted to computer packages Maple and Mathematica - Integrator . In the end, I used contour integration and it took another two days to find the correct contour. I may not publish my solution here, in case I meet some smug kid who badly need to be tormented.

I found the problem here, the given solution is a heuristic argument.

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