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Analyticity of holomorphic functions: Revision history


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  • curprev 16:1616:16, 21 October 2022 128.210.106.65 talk 5,696 bytes +14 The previous statement that the radius of convergence is the distance from the center to the nearest singularity is incorrect. If the singularity is removable, it does not impact the radius of convergence. Call the removable singularity r. Define g(z) to be f(z) for z=/=r and g(r)= lim f(z) as z goes to r (which exists due to r being a removable singularity). The power series for g(z) centered at a is the same as that of f(z). That is, we can "delete" r from consideration. undo

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