DLMF:10.20.E2 (Q3251)

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DLMF:10.20.E2
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    2 3 ⁢ ζ 3 2 = ∫ z 1 1 - t 2 t ⁢ d t = ln ⁡ ( 1 + 1 - z 2 z ) - 1 - z 2 , 2 3 superscript 𝜁 3 2 superscript subscript 𝑧 1 1 superscript 𝑡 2 𝑡 𝑡 1 1 superscript 𝑧 2 𝑧 1 superscript 𝑧 2 {\displaystyle{\displaystyle\frac{2}{3}\zeta^{\frac{3}{2}}=\int_{z}^{1}\frac{% \sqrt{1-t^{2}}}{t}\mathrm{d}t=\ln\left(\frac{1+\sqrt{1-z^{2}}}{z}\right)-\sqrt% {1-z^{2}},}}
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    DLMF:10.20.E2
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