A New Derivation of the Formula solving a Kind of Dirichlet's Problem for a Ring Region

Abstract

In the present short note, an alternative analysis is developed for a kind of DIRICHLET s problem. The problem here considered is that of finding the expression for an analytie function which is everywhere regular in a ring region bounded by two concentric eircles, as we11 as on the bounding circles, and whose real part on the outer circle takes an assigned value and whose imaginary part on the inner circle is nil. It is shown that the formula solving the problem can be derived directly from CAUCHY s theorem, by using in addition RIEMANNSCHWARZ s principle of reflection. In conclusion, I would like to express my thanks to my colleague, Prof. T. SUIMIZU, Mathematical Institute, Osaka Imperial University, for vahuible criticisms