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DLMF:29.1#Ex10 - MaRDI portal

DLMF:29.1#Ex10 (Q9265)

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DLMF:29.1#Ex10
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    DLMF defining formula
    ( s ν m ⁢ ( k 2 ) ) 2 = 4 π ⁢ ∫ 0 K ⁡ ( 𝐸𝑠 ν m ⁡ ( x , k 2 ) ) 2 ⁢ d x . superscript superscript subscript 𝑠 𝜈 𝑚 superscript 𝑘 2 2 4 𝜋 superscript subscript 0 complete-elliptic-integral-first-kind-K 𝑘 superscript Lame-Es 𝑚 𝜈 𝑥 superscript 𝑘 2 2 𝑥 {\displaystyle{\displaystyle(s_{\nu}^{m}(k^{2}))^{2}=\frac{4}{\pi}\int_{0}^{K}% \left(\mathit{Es}^{m}_{\nu}\left(x,k^{2}\right)\right)^{2}\mathrm{d}x.}}
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