Classical anharmonic oscillators: rescaling the perturbation series

A solution to the classical anharmonic-oscillator equation of motion $\stackrel{\ifmmode\ddot\else\textasciidieresis\fi{}}{x}=\ensuremath{-}x\ensuremath{-}\ensuremath{\lambda}{x}^{2n\ensuremath{-}1}$ is obtained by rescaling the perturbation series. The resulting series involves a coupling constant that remains finite for $\ensuremath{\lambda}\ensuremath{\gg}1$ and thus converges rapidly for all $\ensuremath{\lambda}$.