Expansion of the planetary mutual distance raised to any negative power by the method of symbolic differential operators

We present a literal approach to evaluate ^–s necessary for the construction of high order planetary theories. This approach is valid to be applied on very large scale digital computers with standard Poisson series programs, for high order and high degree planetary theories. We apply the method of symbolic differential operators for single variable functions, and the binomial theorem expansions, for the evaluation of ^–s. We utilize Laplace coefficients and its derivatives to carry out the development, without dealing with Newcomb operators or Hansen's coefficients.