1 Basics of Series and Complex Numbers
derivative or integral series is the same as that of the original series. For instance, the geometric series P 1 n=0 z n converges in jzj<1 and its term-by-term derivative P 1 n=0 nz n 1 does also, as you can verify by the ratio test. Taylor Series The Taylor Series of a function f(z) about z= ais f(z) = f(a) + f0(a)(z a) + 1 2 f00(a)(z a)2 ...
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