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Term-wise expectation of the Taylor series for $1/X$ yields asymptotic expansion for $\mathsf EX^{-1}$. What are the conditions?
Migrated from the MSE.
Let $X\sim F_X$ denote a continuous random variable. Computing the first negative moment $\mathsf EX^{-1}$ (assuming it exists) may not be tractable and thus a common tactic is ...
