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This paper resurrects and archives an unpublished original Cornell Laboratoryof Nuclear Studies report by Yuko Okamoto and Richard Talman, "RationalApproximation of the Complex Error Function and the Electric Field of aTwo-Dimensional Gaussian Charge Distribution" CBN 80-13, dating from September1980, during the start-up period of the CESR-CLEO $e^+e^-$ collider. This codehas played a significant role in the calculation of the beam-beam interaction(in particular the beam-beam tune shift) for subsequent storage ring colliders.Electronic access to the (refactored) original codes is provided by activelinks.

Reconstruction: Rational Approximation of the Complex Error Function and the Electric Field of a Two-Dimensional Gaussian Charge Distribution