How can i solve this equation to n ?

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?

Answer 1

[Walter Roberson]

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 )

[Sean de Wolski]

Definitely more optimized than mine. One comment: gammainc() expects (x,a) not(a,x).

Answer 2

[Sean de Wolski]

fzero(@(n)1-(gammainc(x,a)/gamma(n))-R,5)

Maybe? You'll hit overflow if you start with a big n.

Answer 3

[Nick]

Thank you for your answers...

Answer 4

[Nick]

Also, why to put the number 5 to the fzero ? Did you put it randomly ?

[Walter Roberson]

I used it because Sean used it ;-)