Am I missing something? $(\Gamma^{-1})'(y) = \frac{1}{\Gamma '(x)} = \frac{1}{\Gamma(x) \cdot \psi(x)}$ for $y = \Gamma(x)$. The existence of $I$ now immediately follows from the continuity of $\Gamma '$.
Dieter Kadelka
- 2.1k
- 2
- 11
- 15