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Proof of Poisson's Formula

Published online by Cambridge University Press:  24 October 2008

Bengt Åkerberg
Bengt Åkerberg
Affiliation:
Götgatan 61 StockholmSweden
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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

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References

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