作者endlesschaos (佐佐木信二)
看板Math
標題Re: [複變] Laurent series
時間Sat May 21 00:47:09 2011
※ 引述《womack79 (糖做的老虎)》之銘言：
: use laurent series to expand f(z) = 1/(e^z-z-1) at z = 0
: and find converge radius
: 麻煩指點一下hint 感謝
1 1
f(z) = ------------ = -------------------------------------
z z^2 z^3
e - z - 1 1 + z + ----- + ----- + ... - z - 1
2 6
1
= -----------------------------
z^2 z^3 z^4
----- + ----- + ----- + ...
2 6 24
2 1
= ----- * -------------------------------
z^2 z z^4 z^5
1 + --- + ----- + ----- + ...
3 12 60
2 z z^2 z^3 z^4
= ----- * (1 - --- + ----- + ----- - ------ - ...)
(長除法)
z^2 3 36 540 6480
2 2 1 z z^2
= ----- - ---- + ---- + ----- - ------ - ......
z^2 3z 18 270 3240
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1F：推 womack79 :謝謝!! 05/21 00:50