Resummation of scalar correlator in higher spin black hole background

We consider the proposal that predicts holographic duality between certain 2D minimal models at large central charge and Vasiliev 3D higher spin gravity with a single complex field. We compute the scalar correlator in the background of a higher spin black hole at order $\mathcal O(\alpha^{5})$ in the chemical potential $\alpha$ associated with the spin-3 charge. The calculation is performed at generic values of the symmetry algebra $\mbox{hs}[\lambda]$ parameter $\lambda$ and for the scalar in three different representations. We then study the perturbative data in the large $\lambda$ limit and discover remarkable regularities. This leads to formulate a closed formula for the resummation of the leading and subleading terms that scale like $\mathcal O(\alpha^{n}\lambda^{2n})$ and $\mathcal O(\alpha^{n}\,\lambda^{2n-1})$ respectively.