Kepler's equation can be written , where , and where is the eccentric anomaly, is the mean anomaly, n is the mean motion, and e is the orbital eccentricity. Let x be an approximation for the true solution , and let be the error in the guess: . Then we can expand in a Taylor series. For example, to third order we have

This is equivalent to the differential operator form

where the argument in parenthesis is a differential operator with .