\left[1+\left(\frac{x-\gamma}{\beta} \right)^c\right]^{-k-1} and the c.d.f. F(x) = 1-\left[1+\left(\frac{x-\gamma}{\beta} \right)^c \right]^{-k}, the expected shortfall is equal to \operatorname{ES}_\alpha(X) =
