Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T03:18:49.702Z Has data issue: false hasContentIssue false
  • English
  • Français

Proof of Poisson's Formula

Published online by Cambridge University Press:  24 October 2008

Bengt Åkerberg
Bengt Åkerberg
Affiliation:
Götgatan 61 StockholmSweden
Get access Rights & Permissions [Opens in a new window]

Extract

Let f(z)=u(x, y)+iv(x, y) be regular in a domain containing the unit circle C. If where r < 1, then is regular in |z| ≤ 1 and we have and taking real parts and imaginary parts we obtain Poisson's formulae for the harmonic functions u and v.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 1 , January 1961 , pp. 186
Copyright
Copyright © Cambridge Philosophical Society 1961

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

* Carleman, T., Sur les fonctions quasi-analytiques, Conférences faites au cinquième congrès des mathèmaticiens scandinaves (Helsingfors, 1923).Google Scholar