Solution
= Solution
Substituting $z=1$ into the defining <Gamma integral> gives
$$
\boxed{\Gamma(1)=\int_0^{\infty}e^{-t}\,dt=[-e^{-t}]_0^{\infty}=1.}
$$
Both endpoints are convergent, so no continuation of the <Gamma function> is needed here.
= Solution
Substituting $z=1$ into the defining <Gamma integral> gives
$$
\boxed{\Gamma(1)=\int_0^{\infty}e^{-t}\,dt=[-e^{-t}]_0^{\infty}=1.}
$$
Both endpoints are convergent, so no continuation of the <Gamma function> is needed here.