How can i solve this equation to n ?
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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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Walter Roberson
am 3 Feb. 2012
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
am 3 Feb. 2012
Definitely more optimized than mine. One comment: gammainc() expects (x,a) not(a,x).
Sean de Wolski
am 3 Feb. 2012
fzero(@(n)1-(gammainc(x,a)/gamma(n))-R,5)
Maybe? You'll hit overflow if you start with a big n.
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