  We provide analytical tools for pricing power options with exotic features
(capped or log payoffs, gap options ...) in the framework of exponential L\'evy
models driven by one-sided stable or tempered stable processes. Pricing
formulas take the form of fast converging series of powers of the log-forward
moneyness and of the time-to-maturity; these series are obtained via a
factorized integral representation in the Mellin space evaluated by means of
residues in $\mathbb{C}$ or $\mathbb{C}^2$. Comparisons with numerical methods
and efficiency tests are also discussed.
