Abstract
We reconsider black hole solutions of D = 3 higher-spin gravity in the
\$hsłambdahsłambda\$ Chern-Simons formulation. A suitable
generalisation of the BTZ black hole has a spin-3 chemical potential \$\alpha\$,
and non-zero values of all the conserved charges associated with the asymptotic
\$W\_ınftyłambda\$ symmetry. We extend the available perturbative
expansion of the partition function to order \$O(\alpha^18)\$ for
generic values of the \$łambda\$ parameter. The result matches the CFT
prediction at \$łambda=0\$ and at \$łambda=1\$ where we provide the exact
all-order expansion of the partition function. The perturbative series is then
analysed in the interesting non-trivial limit \$łambda\toınfty\$ and we derive
the exact analytical expressions of the partition function and the spin-4
charge in closed form as functions of \$\alpha\$. Also, the first subleading
correction at large \$łambda\$ is shown to be simply related to the leading
contribution.
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