Some probabilistic methods are used to find a number of combinatorial identities in very elementary manners. One of the identities is for the Laplace transform of a suitable sequence of ordered random variables from an exponential distribution. This identity leads to Gauss’s product formula for gamma function, which itself provides many interesting formulas. Some asymptotics of the underlying distribution are described in connection with some of these identities and Gauss’s product formula.
Exponential distribution Ordered sequence Combinatorial identities Asymptotic Moment generating function Product formula
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