Eine verallgemeinerte Darboux-Gleichung I |
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Authors: | Prof Dr Karl Wilhelm Bauer |
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Institution: | 1. Lehrkanzel und Institut für Mathematik, Technische Hoschule in Graz, Kopernikusgasse 24, A-8010, Graz, ?sterreich
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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. |
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