Understand
In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space.
- In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function consistent with the both expansions, which includes the standard Pad\'e approximant and fractional power of polynomial method constructed by Sen as special cases.
- We point out that we can construct enormous number of such interpolating functions in principle while the "best" approximation for the exact answer of the physical quantity should be unique among the interpolating functions.
- We propose a criterion to determine the "best" interpolating function, which is applicable except some situations even if we do not know the exact answer.