What is $$\mathfrak L (\Gamma(z))$$? And how can it be derived?
$$\Gamma(z)=\int_0^\infty t^{z-1}e^t dt$$
$$\mathfrak L(\Gamma(z)) = \int_0^\infty \int_0^\infty t^{z-1}e^t dt e^{-sz} dz$$
Yes, of course I tried to find on google but I could only find something like laplace transform using the gamma function, and inverse Laplace transform of gamma function, etc..
Also I tried by myself, but no fruit..
This result may be applied to solving gamma functional equation, which is in another question.
$\endgroup$ 71 Answer
$\begingroup$You can't find it because it does not exist:$$\lim_{n \to \infty} \frac{n!}{e^{an}}=\infty \quad \forall a \in \mathbb{R}$$
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