Partial self inductance at DC of some common cross sections

The partial self inductance per unit of length at DC is developed, for a long conductor, into a series with a logarithmic and constant term and inverse powers of the length, involving characteristic distances: geometrical and arithmetical mean distance, and higher orders. This is applied to some common conductor cross sections: ellipse, rectangle and diamond, for which analytical and approximate expressions are provided. In the limit of zero thickness the inductance and characteristic distances still depend on the originating cross section.