Complex Analysis: Theory and Applications · Problem 4.4.5

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · radius-of-convergence

Problem

Suppose that ∑n=0∞cnzn\displaystyle\sum_{n=0}^{\infty} c_n z^n has radius of convergence RR. Show that ∑n=0∞cn2zn\displaystyle\sum_{n=0}^{\infty} c_n^2 z^n has radius of convergence R2R^2.

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