Abstract
A computer program for the manipulation of power series in several variables is used to find the first order solution to Hill's lunar problem. The ratiom of the mean motion of the Sun to that of the Moon is kept as a formal parameter. The series inm are known to converge very poorly. It is shown how efficient algorithms among them the Lie transformation allow us to compute the series inm as far as they are needed. When the series are evaluated at Brown's numerical value form the results achieve or exceed his accuracy.
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