Naturally occurring continued fractions in the variation of Kepler's equation

A family of functions involving integrals of universal functions is introduced. These functions have some interesting mathematical properties including the fact that they may be expressed as Gaussian continued fractions. An unique method of performing the integration is demonstrated which indicates why these functions may be important in the variation of Kepler's equation.This work was supported at the Charles Stark Draper Laboratory, Inc. by the National Aeronautics and Space Administration under Contract NAS9-17560.