Sierpiński constant

The Sierpiński constant $S$ is given by $$S=\log \left( \dfrac{4\pi^3 e^{2\gamma}}{[\Gamma(\frac{1}{4})]^4} \right),$$ where $\log$ denotes the logarithm, $\pi$ denotes pi, $e$ denotes e, $\gamma$ denotes the Euler-Mascheroni constant, and $\Gamma$ denotes the gamma function.