  The closed Dyson-Schwinger equation for the 2-point function of the
noncommutative $\lambda \phi^4_2$-model is rearranged into the boundary value
problem for a sectionally holomorphic function in two variables. We prove an
exact formula for a solution in terms of Lambert's $W$-function. This solution
is holomorphic in $\lambda$ inside a domain which contains $(-1/\log
4,\infty)$. Our methods include the Hilbert transform, perturbation series and
Lagrange-B\"urmann resummation.
