Abstract In Part I, a large parameter asymptotic expansion of a perturbed simple harmonic oscillator is presented. Perturbations of the form λx∝ are studied were λ is the coupling constant. The method is demonstrated by a general derviation of the wavefunctions to third order for any ∝ and quantum number n. Additonal expressions are presented for the ground states to tenth order in the energy. It is also shown that the "matching condition" for the basic and...