I asked the same thing on Physicsforums, I am hoping for some feedback here as well.
I saw this method of calculating:
\(\displaystyle \displaystyle{I = \int_{0}^{1} \log^2(1-x)\log^2(x) dx}\)
http://math.stackexchange.com/questions/959701/evaluate-int1-0-log21-x-log2x-dx
Can you take a look at M.N.C.E.'s method?
I dont understand a few things.
Somehow he makes the relation:
\(\displaystyle \displaystyle{\frac{4H_n}{(n+1)(n+2)^3} = \frac{\left( \gamma + \psi(-z) \right)^2}{(z+1)(z+2)^3}}\)
How is this established?
And this I dont understand, why did he integrate it,?
And then after he states: "At the positive integers," what is he doing with the residues. I know the residue theorem etc, but I dont understand what he is exactly doing?
Thanks
I saw this method of calculating:
\(\displaystyle \displaystyle{I = \int_{0}^{1} \log^2(1-x)\log^2(x) dx}\)
http://math.stackexchange.com/questions/959701/evaluate-int1-0-log21-x-log2x-dx
Can you take a look at M.N.C.E.'s method?
I dont understand a few things.
Somehow he makes the relation:
\(\displaystyle \displaystyle{\frac{4H_n}{(n+1)(n+2)^3} = \frac{\left( \gamma + \psi(-z) \right)^2}{(z+1)(z+2)^3}}\)
How is this established?
And this I dont understand, why did he integrate it,?
And then after he states: "At the positive integers," what is he doing with the residues. I know the residue theorem etc, but I dont understand what he is exactly doing?
Thanks
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