Carson's integral

Exact computation of the earth return impedance of overhead conductors above homogeneous earth.

Carson's integral is used in power systems analysis for evaluating the earth-return impedance of overhead conductors above homogeneous earth. Contrary to the widespread belief that it does not evaluate to a closed-form expression, a scrutiny of Carson's historical (1926) paper reveals that such an expression exists and was actually presented therein. Functions Carson_Self and Carson_Mutual compute exactly both the total earth-return impedance (self and mutual) and Carson's integral. The computation is based on the exact evaluation of Struve functions of complex argument by the same author. SInce these are computed to machine accuracy, Carson's integral is also computed to the highest precision.