Is the Legendre-Fenchel transform of $$f(x)=1-\sqrt{1-|x|^2}, x\in B(0,1)\subset\mathbb{R}^n$$ just $$f^*(x^*)=-1+\sqrt{1+|x^*|^2}?$$
I calculated this using the table here http://en.wikipedia.org/wiki/Convex_conjugate#Table_of_selected_convex_conjugates
but I'm not sure if what I did was legal becauseit only gives some functions for $\mathbb{R}$.