DLMF:19.20.E2 (Q6376)

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DLMF:19.20.E2
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    ∫ 0 1 d t 1 - t 4 = R F ⁡ ( 0 , 1 , 2 ) = ( Γ ⁡ ( 1 4 ) ) 2 4 ⁢ ( 2 ⁢ π ) 1 / 2 = 1.31102 87771 46059 90523 ⁢ … . superscript subscript 0 1 𝑡 1 superscript 𝑡 4 Carlson-integral-RF 0 1 2 superscript Euler-Gamma 1 4 2 4 superscript 2 𝜋 1 2 1.31102 87771 46059 90523 … {\displaystyle{\displaystyle\int_{0}^{1}\frac{\mathrm{d}t}{\sqrt{1-t^{4}}}=R_{% F}\left(0,1,2\right)=\frac{\left(\Gamma\left(\frac{1}{4}\right)\right)^{2}}{4(% 2\pi)^{1/2}}=1.31102\;87771\;46059\;90523\;\dots.}}
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    DLMF:19.20.E2
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