- #1
Amad27
- 412
- 1
I saw this method of calculating:
$$I = \int_{0}^{1} \log^2(1-x)\log^2(x) dx$$
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 don't understand a few things.
Somehow he makes the relation:
$$\frac{4H_n}{(n+1)(n+2)^3} = \frac{\left( \gamma + \psi(-z) \right)^2}{(z+1)(z+2)^3}$$
How is this established?
And this I don't 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 don't understand what he is exactly doing?
Thanks
$$I = \int_{0}^{1} \log^2(1-x)\log^2(x) dx$$
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 don't understand a few things.
Somehow he makes the relation:
$$\frac{4H_n}{(n+1)(n+2)^3} = \frac{\left( \gamma + \psi(-z) \right)^2}{(z+1)(z+2)^3}$$
How is this established?
And this I don't 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 don't understand what he is exactly doing?
Thanks