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Q30Section II (Mathematics)30 of 180

Weierstrass's theorem — uniform limits of analytic functions are analytic

Let G be a region and suppose fn:G→Cf_n:G\to\mathbf C is analytic for each n≥1n\ge1. Suppose {fn}\{f_n\} converges uniformly to a function f:G→Cf:G\to\mathbf C. Then:

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