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We study positive random variables whose moments can be expressed by productsand quotients of Gamma functions; this includes many standard distributions.General results are given on existence, series expansion and asymptotics ofdensity functions. It is shown that the integral of the supremum process ofBrownian motion has moments of this type, as well as a related random variableoccuring in the study of hashing with linear displacement, and the generalresults are applied to these variables.

Moments of Gamma type and the Brownian supremum process area