We consider an analogue of Kontsevich's matrix Airy function where the cubic potential $\mathrm{Tr}(\Phi^3)$ is replaced by a quartic term $\mathrm{Tr}(\Phi^4)$. We show that, for finite matrices, all cumulants are exactly solvable in terms rational functions, their branch points and their inverses. For the planar sector we also control the limit to infinite matrices where generating functions of hyperlogarithms are produced.
Nguyen-Viet Dang