Iterative integration of Laplace's equation within symmetric boundaries

J.R. Pierce Theory and design of electron beams Van Nostrand New York 1954 is perhaps the most accessible reference J.R. Pierce Rectilinear electron flow in beams Journal for Applied Physics August 1940 Contains the conformal transformation solution given here as a check

E. Jahnke F. Emde Tables of functions 4th edition Dover New York 1945