  The divergent series for a function defined through Lapalce integral and the
ground state energy of the quartic anharmonic oscillator to large orders are
studied to test the generalized binomial transform which is the renamed version
of $\delta$-expansion proposed recently. We show that, by the use of the
generalized binomial transform, the values of functions in the limit of zero of
an argument is approximately computable from the series expansion around the
infinity of the same argument. In the Laplace integral, we investigate the
subject in detail with the aid of Mellin transform. In the anharmonic
oscillator, we compute the strong coupling limit of the ground state energy and
also the expansion coefficients at strong coupling from the weak coupling
perturbation series. The obtained result is compared with that of the linear
delta expansion.
