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 $(\Gamma^{-1})'$.
Dieter Kadelka
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