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The list contains values of the Gamma function $\Gamma(s)$ at rational number $s = a/b$. For $\Re(s) > 0$, $\Gamma(s)$ is defined as the Mellin transform of $e^{-t}$, that is, $\Gamma(s) = \int_0^\infty t^s e^{-t}\, (dt/t)$. $\Gamma$ extends to a meromorphic function on $\mathbb{C}$ via analytic continuation.
Parameters
$s$
— rational number ($s \not \in \mathbb{Z}_{\leq 0}$)
Formulas
(1)
$\Gamma(s+1) = s\Gamma(s)$ for all $s\in\mathbb{C}$.