Shifting a series
- Jonathan Holland
A given rational function has a power series expansion centered at the origin, with radius of convergence 1. If we move the expansion point to x=1, what are the constraints on the radius of convergence of the new series?
Answer: The radius of convergence of the shifted series is a real number r in [0,2]. It can assume any real value r in this range, for a suitable choice of rational function (shown).