Say we have two power series [itex]\sum_{n=0}^{\infty}a_n z^n[/itex] and [itex]\sum_{n=0}^{\infty}b_n z^n[/itex] which both converge in the open unit disk. Is there anything we can say about the radius of convergence of the power series formed by their difference? i.e. [itex]\sum_{n=0}^{\infty}(a_n-b_n) z^n[/itex](adsbygoogle = window.adsbygoogle || []).push({});

What about if we know that their difference is bounded on compact sets? i.e. [itex]|\sum_{n=0}^{\infty}(a_n-b_n) z^n| < M[/itex] for all z in a compact subset of the open unit disk.

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# Subtraction of Power Series

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