请问log(2,m!)的近似值

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log(2,1)+log(2,2)...+log(2,m) =log(2,1*2...*m) =log(2,m!) m比较大时m!很难算

wayne

$\frac{1}{2} \log_2(2 \pi(m+\frac{1}{6}))+m \log_2(\frac{m}{e})$

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怎么推导的?

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SQL> with t as 2 ( 3 select 1 a,1 b from dual union all 4 select 2 a,2 b from dual union all 5 select 3 a,6 b from dual union all 6 select 4 a,24 b from dual union all 7 select 5 a,120 b from dual union all 8 select 6 a,720 b from dual union all 9 select 7 a,5040 b from dual union all 10 select 8 a,40320 b from dual union all 11 select 9 a,362880 b from dual union all 12 select 10 a,3628800 b from dual) 13 select a,log(2,b),1/2*log(2,(a+1/6)*asin(1)*2*2)+a*log(2,(a/exp(1))) from t; A LOG(2,B) 1/2*LOG(2,(A+1/6)*ASIN(1)*2*2)+A*LOG(2,(A/EXP(1))) ---------- ---------- -------------------------------------------------- 1 0 -.00575077 2 1 .998096592 3 2.5849625 2.58403295 4 4.5849625 4.58441475 5 6.9068906 6.90653024 6 9.4918531 9.49159826 7 12.299208 12.2990184 8 15.299208 15.2990614 9 18.469133 18.4690163 10 21.7910611 21.790966

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真的很近似

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$\frac{1}{2} \log _2(2 \pi (m+\frac{1}{6}))+m \log _2(\frac{m}{e})$ wayne 发表于 2010-3-12 10:28

怎么看了有4个[?]

mathe

这个叫stirling公式.论坛里面已经出现多次了

KeyTo9_Fans

wayne不是问过这个问题了吗？ 楼主还要问，真是不应该啊。 见 http://bbs.emath.ac.cn/viewthread.php?tid=2090&fromuid=1394 已详细解答。

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我第一次遇到一个实际问题,就是往一个平衡2叉树插入顺序新值的时间复杂度