Eine verallgemeinerte Darboux-Gleichung II

Abstract

The paper is concerned with the elliptic equation

$$\begin{gathered} w_{z\bar z} + \left[ {\frac{{n(n + 1)}}{{(z - \bar z)^2 }} - \frac{{m(m + 1)}}{{(z + \bar z)^2 }} + \frac{{q(q + 1)}}{{(1 + z\bar z)^2 }} - \frac{{p(p + 1)}}{{(1 - z\bar z)^2 }}} \right]w = 0, \hfill \\ n,m,p,q \in \mathbb{N}_0 . \hfill \\ \end{gathered}$$

General representation theorems for the solutions are derived by differential operators if three parameters are different from zero or two parameters are equal. Some applications are given to pseudo-analytic functions and generalized Tricomi equations.