For random variable $Z$ from a $Gamma(p), p > 0$ distribution we know that the expected value of $E[Z^s]$ is simply the gamma function at $p+s$ divided by the gamma function at $p$, for $p+s$ > 0.
But what if we are interested in calculating $E[Z^{-2}]$ and the variance of $Z^{-2}$ ? We can just use the same method requiring $p > 2$, but is there a more general way of evaluating in the case that $p < 2$?
