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I am investigating exact and approximation methods to compute a Laplace–Stieltjes transform of various distributions. I know that it is easy for an exponential distribution, but I am confused for a beta distribution for example.

I'd really appreciate if you could give me some directions and references to follow.

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I often see convolutions of exponential distributions, so there is value in computing the transforms of an exponential distribution. I don't know of nearly as many situations where I would convolve a beta distribution with something. How would you use the Laplace transform of a beta distribution? At least for integer parameters you can compute it by integration by parts, but I think it's messy in general involving hypergeometric functions. – Douglas Zare Aug 26 '12 at 19:53

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