Perturbative solutions of $\mathcal{N}=1^{\ast }$ holography on $S^4$

We apply the recently proposed perturbative technique to solve the supergravity BPS equations of $\mathcal{N}=1^{\ast }$ theories put on $S^4$. In particular, we have calculated the coefficients of the leading quartic terms exactly, in the expression of the universal part for the holographic free energy as a function of the mass parameters. We also report on the coefficients of higher order terms upto 10th order, which are computed numerically.