### A class of logarithmically completely monotonic functions associated with a gamma function.

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A number of properties of a function which originally appeared in a problem proposed by Ramanujan are presented. Several equivalent representations of the function are derived. These can be used to evaluate the function. A new derivation of an expansion in inverse powers of the argument of the function is obtained, as well as rational expressions for higher order coefficients.

We give higher-power generalizations of the classical Lerch formula for the gamma function.

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