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PDF file75 Taylor series examples The uniqueness of Taylor series along with the fact that they converge on any disk around z 0 where the function is analytic allows us to use lots of computational tricks to nd the series and be sure that it converges Example 77 Use the formula for the coe cients in terms of derivatives to give the Taylor series of f(z) = ez around z= 0 Solution Since f0(z) = ez.
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PDF filePower series (Sect 107) I Power series definition and examples I The radius of convergence I The ratio test for power series I Term by term derivation and integration Power series definition and examples Definition A power series centered at x 0 is the function y D ⊂ R → R y(x) = X∞ n=0 c n (x − x 0)n c n ∈ R Remarks I An equivalent expression for the power series is.
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