# Shifting a series

- Author:
- 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).

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