Summary: This paper examines an attractive delta-function potential in \(D\)-dimensional space, where \(D\) is regarded as an arbitrary complex number. The renormalized scattering amplitude is calculated for arbitrary \(D\) and is shown to be finite as \(D\to 2\). Dimensional expansions about \(D=0\) and \(D=2\) are obtained; these expansions have a non-zero radius of convergence.