  We calculate analytically properties of holographic superconductors in the
probe limit. We analyze the range $1/2 < \Delta < 3$, where $\Delta$ is the
dimension of the operator that condenses. We obtain the critical temperature in
terms of a solution to a certain eigenvalue problem. Near the critical
temperature, we apply perturbation theory to determine the temperature
dependence of the condensate. In the low temperature limit we show that the
condensate diverges as $T^{-\Delta/3}$ for $\Delta < 3/2$ whereas it asymptotes
to a constant value for which we provide analytic estimates for $\Delta > 3/2$.
We also obtain the frequency dependence of the conductivity by solving
analytically the wave equation of electromagnetic perturbations. We show that
the real part of the DC conductivity behaves as $e^{-\Delta_g /T}$ and estimate
the gap $\Delta_g$ analytically. Our results are in good agreement with
numerical results.
