DLMF:19.30.E11 (Q6686)

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DLMF:19.30.E11
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    Statements

    Defining formula
    s = 2 ⁢ a 2 ⁢ ∫ 0 r d t 4 ⁢ a 4 - t 4 = 2 ⁢ a 2 ⁢ R F ⁡ ( q - 1 , q , q + 1 ) , 𝑠 2 superscript 𝑎 2 superscript subscript 0 𝑟 𝑡 4 superscript 𝑎 4 superscript 𝑡 4 2 superscript 𝑎 2 Carlson-integral-RF 𝑞 1 𝑞 𝑞 1 {\displaystyle{\displaystyle s=2a^{2}\int_{0}^{r}\frac{\mathrm{d}t}{\sqrt{4a^{% 4}-t^{4}}}=\sqrt{2a^{2}}R_{F}\left(q-1,q,q+1\right),}}
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    DLMF id
    DLMF:19.30.E11
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    constraint
    q = 2 ⁢ a 2 / r 2 = sec ⁡ ( 2 ⁢ θ ) 𝑞 2 superscript 𝑎 2 superscript 𝑟 2 2 𝜃 {\displaystyle{\displaystyle q=2a^{2}/r^{2}=\sec\left(2\theta\right)}}
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