Some asymptotic formulae given elsewhere for the zeros of the incomplete gamma function
γ
(
a
,
x
)
\gamma (a,x)
are corrected. A plot of a few of the zero trajectories of the function
γ
(
x
w
,
x
)
\gamma (xw,x)
is given, where
x
x
is a real parameter. Based on theoretical work by Mahler, it is seen that the zero trajectories of
γ
(
x
w
,
x
)
\gamma (xw,x)
lie in a finite region of the complex
w
w
-plane.