Convergence from Divergence

Understand

We show how to convert divergent series, which typically occur in many applications in physics, into rapidly convergent inverse factorial series.

• This can be interpreted physically as a novel resummation of perturbative series.
• Being convergent, these new series allow rigorous extrapolation from an asymptotic region with a large parameter, to the opposite region where the parameter is small.
• We illustrate the method with various physical examples, and discuss how these convergent series relate to standard methods such as Borel summation, and also how they incorporate the physical Stokes phenomenon.