  We introduce a transformation for converting a series in a parameter,
\lambda, to a series in the inverse of the parameter \lambda^{-1}. By applying
the transform on simple examples, it becomes apparent that there exist
relations between convergent and divergent series, and also between large- and
small-coupling expansions. The method is also applied to the divergent series
expansion of Euler-Heisenberg-Schwinger result for the one-loop effective
action for constant background magnetic (or electric) field. The transform may
help us gain some insight about the nature of both divergent (Borel or
non-Borel summable series) and convergent series and their relationship, and
how both could be used for analytical and numerical calculations.
