  The technique of complex scaling for time harmonic wave type equations relies
on a complex coordinate stretching to generate exponentially decaying
solutions. In this work, we use a Galerkin method with ansatz functions with
infinite support to discretize complex scaled Helmholtz resonance problems. We
show that the approximation error of the method decays super algebraically with
respect to the number of unknowns in radial direction. Numerical examples
underline the theoretical findings and show the superior efficiency of our
method compared to a standard perfectly matched layer method.
