Gamma and incomplete gamma functions- when are they equal?

Question

I do not know anything about these gamma functions. In a series sum I got two terms as follows: $\Gamma(b/c) - \Gamma(b/c,a/c)$. The first is a gamma function, the second is an incomplete gamma function. I know $a,b,c>0$ and $b>a, b>c$. When (what conditions I need) is the expression I wrote above equal to $0$?

Answer 1

$\Gamma(b/c,a/c)=\Gamma(b/c)$ if $a/c=0.$ So in your case they are never equal.

PS: The function $\gamma(b/c,a/c) = \Gamma(b/c)-\Gamma(b/c,a/c)$ is the lower incomplete gamma function, this function has zeroes for $b/c < 0$.