File:Natural boundary example.gif

(Approximate) plot of the modulus of the function for ${\displaystyle {\displaystyle \sum _{n=0}^{\mathrm{\infty }}}{z}^{2^n}}$ in the closed unit zero-centred circle. Natural boundary as the unit circumference is shown, together as its convergence rates azimuthally differing according to the powers-of-2's complex exponentials.

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