The observation by Poincaré that Möbius transformations in the complex plane can be lifted to a half-space raises the need to be able to handle motions in hyperbolic space of more than two dimensions by means of an analytic apparatus of not too forbidding complexity. In my experience the best way to do so is to be guided by analogies with the familiar twodimensional case. The purpose of this little paper is to collect a few formulas that the writer has found useful when working with certain hyperbolically invariant operators.