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x/(1+x-2x^3) 展成x的幂级数
人气:419 ℃ 时间:2020-03-25 02:01:20
解答
f(x) = x/(1+x-2x^3) = x/[(1-x)(1+2x+2x^2)]= (1/5)[1/(1-x)+(-1+2x)/(1+2x+2x^2)],后项在实数域内不能分解,故只能在复数域内分解展开成幂级数 f(x) = (1/5)/(1-x) - [(1+5i)/10]/[1+(1-i)x/2] + [(-1+5i)/10]/[1+(...
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