Lambert-W solves the noncommutative phi^4-model

The closed Dyson-Schwinger equation for the 2-point function of the noncommutative λφ^4-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 λ inside a domain which contains (−1/log 4,∞). Our methods include the Hilbert transform, perturbation series and Lagrange- Bürmann resummation.