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

Resummation of scalar correlator in higher spin black hole background