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How can i solve this equation to n ?

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Nick
Nick 2012-2-3
编辑： T 2013-10-11
I try to solve this equation 1-(γ(a,x)/(n-1)!)=R to n but i can't find how, where R>=0 and γ(a,x) is the lower incomplete gamma function as i found. Does anyone have any idea?

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回答（4 个）

Walter Roberson
Walter Roberson 2012-2-3
If 1-(γ(a,x)/(n-1)!)=R then 1 + R = y(a,x) / (n-1)! and so
(n-1)! = y(a,x) / (1 + R);
(n-1)! is gamma(n), so you want to solve gamma(n) = y(a,x) / (1+R)
c = gammainc(a,x) / (1+R);
fzero( @(n) gamma(n) - c, 5 )
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Sean de Wolski
Sean de Wolski 2012-2-3
Definitely more optimized than mine. One comment: gammainc() expects (x,a) not(a,x).

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Sean de Wolski
Sean de Wolski 2012-2-3
fzero(@(n)1-(gammainc(x,a)/gamma(n))-R,5)
Maybe? You'll hit overflow if you start with a big n.
Nick
Nick 2012-2-13
Thank you for your answers...
Nick
Nick 2012-2-14
Also, why to put the number 5 to the fzero ? Did you put it randomly ?

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