A Closed-Form Solution To Kepler's Equation (Preprint)

A short paper that derives a closed form solution to Kepler's equation derived from Lagrange's inversion theorem, this, by applying the inverse mellin transform over the mellin transform of said formula, and then manipule it until it reaches a state that can actually be used, while still being an exact answer. Note: the Cauchy's residue series used to prove the method is only for infinite polynomials with integer powers, nevertheless, the integral representation works for all cases; And the domain of application for the integral is limited if the inverse has an asymptote in the real line.