  For a spectrally positive and strictly stable process with index in (1,2), a
series representation is obtained for the joint distribution of the "first
passage triple" that consists of the time of first passage and the undershoot
and the overshoot at first passage. The result leads to several corollaries,
including 1) the joint law of the first passage triple and the pre-passage
running supremum, and 2) at a fixed time point, the joint law of the process'
value, running supremum, and the time of the running supremum. The
representation can be decomposed as a sum of strictly positive functions that
allows exact sampling of the first passage triple.
