# Relation between two gamma functions

Does anyone know the relation between these two gamma functions?

1st) Gamma[1 + c, a (1 + b)]

2nd) Gamma[c, a (1 + b)]

The question is: may I write the 1st like the 2nd times something?

thank you very much

Let's note $x:=a(1+b)$ then for positive $c$ and $x$ we have : $$\Gamma(1 + c,\; x)-c\;\Gamma( c,\, x)=x^c\;e^{-x}$$