Express 1/(a^2+x^2) in cvx

Indeed, it is only convex for x^2 \ge a^2/3 (which, although only mattering as a piece of trivia, is itself a non-convex region).

I guess this is another expression for @Erling’s challenge., which, as shown below, does not exclude expressions which are not convex over their entire natural domain. Maybe the challenge should be clarified to include that provision.

Conic modeling challenge by Do you have a nonlinear constraint that can be written in a modeling language, but can’t be represented with linear, socp, sdp, exponential cone and power cones?