  A multiplicative identity in law connecting the hitting times of completely
asymmetric $\alpha-$stable L\'evy processes in duality is established. In the
spectrally positive case, this identity allows with an elementary argument to
compute fractional moments and to get series representations for the density.
We also prove that the hitting times are unimodal as soon as $\alpha\le 3/2.$
Analogous results are obtained, in a much simplified manner, for the first
passage time across a positive level.
