Green’s function for the semi-infinite strip in terms of an improper integral

Abstract

In this paper Green?s function for the semi-infinite strip (which is the two-dimensional Green?s function for a groove of infinite depth and length) is determined in the form of an improper integral, as opposed to the standard summation form. The integral itself, although rather complex, is found in a closed form. By using the derived Green?s function simple formulas are obtained for a single and two-wire line configurations inside the groove.