  The renormalization group method is applied for obtaining the asymptotic form
of the wave function of the quantum anharmonic oscillator by resumming the
perturbation series. It is shown that the resumed series is the cumulant of the
naive perturbation series. Working out up to the sixth order and performing a
further resummation proposed by Bender and Bettencourt, we find that the
agreement with the WKB result becomes worse in the higher orders than the
fourth at which the agreement is the best.
