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.
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