Question

Why gamma gunction is not defined for negative integers?

Answer 1

From wikipedia equation may be in Latex, but that part didn't copy) Although the Gamma function is defined for all complex numbers except the non-positive integers, it is defined via an improper integral that converges only for complex numbers with a positive real part: \Gamma(z) = \int_0^\infty t^{z-1} e^{-t}\,{\rm d}t\,. 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

Reference https://www.physicsforums.com/threads/gamma-function-on-negative-fractions.489613/