Solving Infinite Integral - Get Help Here!

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    Infinite Integral
romeo6
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Hey folks, can anyone give me some pointers with the following:

-\frac{1}{2}\sum_{m,n}\frac{\partial}{\partial s}|_{s=0}\int\frac{d^4k}{(2\pi)^4}(k^2+M^2_{m,n})^{-s}

=-\frac{1}{32\pi^2}\frac{\partial}{\partial s}|_{s=-2}\frac{1}{s(s+1)}\sum_{m,n}(M_{m,n}^2)^{-s}

Any hints here would be great, my Schaums isn't coming in too useful here.

Thanks!
 
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What is it that you're trying to show? Equality? At the moment this doesn't mean anything - you need to properly define the problem. Until then it's impossible to help you.
 
Well, I'm trying to understand how the k integral was done.

If its any help its from equation 1 of http://arxiv.org/abs/hep-ph/0301168
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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