Gamma Function is Smooth on Positive Reals

Theorem

Let $\Gamma: \R_{>0} \to \R$ be the Gamma function, restricted to the strictly positive real numbers.


Then $\Gamma$ is smooth.


This article is complete as far as it goes, but it could do with expansion.
In particular: I'm quite sure it's analytic on all of its domain
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Proof


This theorem requires a proof.
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Sources

  • 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $11.14 \ \text{(ii)}$
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