Let $f: \mathbf{R} \to \mathbf{R}$ be an analytic function. Is there a rotationally symmetric harmonic function $u$ on the circular cylinder $D \times \mathbf{R} \subset \mathbf{R}^3$ so that $u = f$ along the axis of rotation $\{ (0,0) \} \times \mathbf{R}$?