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We investigate a recursively generated sequence of random variables thatbegins with an Exponential random variable with parameter (i.e., inverse-mean)1, and continues with additional Exponentials, each of whose random parameterpossesses the distribution of the prior term in the sequence. Although suchsequences enjoy some (limited) applicability as models of parameteruncertainty, our present interest is primarily theoretical. Specifically, weobserve that the implied sequence of distribution functions manifests asurprising connection to two well-known mathematical quantities first studiedby Leonhard Euler: the Euler-Gompertz and Euler-Mascheroni constants. Through aclose analysis of one member of this distribution-function sequence, we areable to shed new light on these constants.

A Sequence of Nested Exponential Random Variables with Connections to Two Constants of Euler