Download - 第三节 Taylor 级数
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1 Taylor2 Taylor Taylor
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Taylor. , . Taylor. . 3.1 Taylor
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.R(D, R=+), cn
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.C.R r>0, z0, r
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Cauchy
2.5 f (z)D,
z0 D, C z0
() Jordan,
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C.
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C.C
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4.10 z0Taylor, R=|z0-a|, a z0 f (z).
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Taylor Taylor.
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3.2 TaylorTaylor:1. ; 2. .1. Taylor f (z)z0 .
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2. , , (, ) () , Taylor.: , , .
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3.2
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Taylor.
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Taylor. .
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z=0Taylor. . , :
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z=0,
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Taylor.
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MATLAB.>> syms z;>> f=z/(z+1);>> taylor(f,z,4,1) % z=14 ans = 1/4+1/4*z-1/8*(z-1)^2+1/16*(z-1)^3
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: Taylor