  When we have two expansions of physical quantity around two different points
in parameter space, we can usually construct a family of functions, which
interpolates the both expansions. In this paper we study analytic structures of
such interpolating functions and discuss their physical implications. We
propose that the analytic structures of the interpolating functions provide
information on analytic property and Stokes phenomena of the physical quantity,
which we approximate by the interpolating functions. We explicitly check our
proposal for partition functions of zero-dimensional $\varphi^4$ theory and
Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our
result with a recent result from resurgence analysis. We also comment on
construction of interpolating function in Borel plane.
