# Hyperbolic function theory in the plane

Presenter: **Vesa Vuojamo**, Tampere University of Technology, Finland

Joint work with **Sirkka-Liisa Eriksson, Heikki Orelma**

We study generalized analytic functions and hyperbolic harmonic functions in the upper half plane and generalize the results to higher dimensions. Hyperbolic harmonic functions are solutions of the equation $$\Delta u-\frac{\alpha}{y}\partial_yu=0$$
where $\alpha$ is a real parameter.
We consider solutions which depend only on the hyperbolic distance and represent these using Legendre functions.