\[\int_{0}^{1}\frac{t^{2}\,\mathrm{d}t}{\sqrt{1-t^{4}}}=\tfrac{1}{3}R_{D}\left(0%
,2,1\right)=\frac{\left(\Gamma\left(\frac{3}{4}\right)\right)^{2}}{(2\pi)^{1/2%
}}=0.59907\;01173\;67796\;10371\dots.\]