$\begingroup$ when i'm using Euler's reflection formula $\Gamma(1/4)$ appears which i'm unable to solve again
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$\begingroup$ This PDF is great for finding these values real quick. Taking a quick look, we have:
$$\Gamma\left(\frac14\right)=2\sqrt[4]\pi\sqrt{K\left(\frac1{\sqrt2}\right)}$$
where $K()$ is an elliptic integral of the first kind.
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