From a journal, they proved this equality:
$ \frac{z}{\alpha -1}\left(\int_0^1 \frac{t^{\frac{1}{\alpha}}}{1-tz} dt -\alpha \int_0^1 \frac{v}{1-vz} dv\right) = \int_0^1 t^{\frac{1}{\alpha}} \left(\int_0^1 \frac{vz}{1-tvz}dv\right)dt $
I already tried various methods to prove it but I can't get the same equality. Do you have any idea? I really need to refer this journal to assist my research. Thank you.