lnx=ln(x-1+1)=(x-1)-(x-1)^2/2+(x-1)^3/3-.
1/x=1/(1+x-1)=1-(x-1)+(x-1)^2-(x-1)^3+.
設(shè)ln(x)/x=a0+a1(x-1)+a2(x-1)^2+a3(x-1)^3+.
[(x-1)-(x-1)^2/2+(x-1)^3/3-.]
=[a0+a1(x-1)+a2(x-1)^2+a3(x-1)^3+.][1-(x-1)+(x-1)^2-(x-1)^3+.]
比較系數(shù)得：a0=0,a1-a0=1,a2+a0-a1=-1/2,.
ln(x)/x=(x-1)+(x-1)^2/2+.
求ln(x)/x關(guān)于x-1的冪級(jí)數(shù)展開式
求ln(x)/x關(guān)于x-1的冪級(jí)數(shù)展開式
數(shù)學(xué)人氣：643 ℃時(shí)間：2020-06-06 11:05:47
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