From your other answer it sounds like that you know what the OP means? I'll bite anyway ... The Wikipedia article on the gamma function https://en.wikipedia.

From your other answer it sounds like that you know what the OP means? I'll bite anyway ... The Wikipedia article on the gamma function https://en.wikipedia.org/wiki/Gamma_function https://en.wikipedia.org/wiki/Gamma_function states that "The gamma function is defined for all complex numbers except the non-positive integers. For complex numbers with a positive real part, it is defined via a convergent improper integral ..." So maybe that is what the OP means: the gamma function Γ(z) can be defined by via convergent improper integral for all complex numbers of z with real part greater than zero. ? Wikipedia then points out that: "This integral function is extended by analytic continuation to all complex numbers except the non-positive integers (where the function has simple poles), yielding the meromorphic function we call the gamma function."