DLMF:23.11.E2 (Q7321)

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DLMF:23.11.E2
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    ( z ) = 1 z 2 + 8 0 s ( e - s sinh 2 ( 1 2 z s ) f 1 ( s , τ ) + e i τ s sin 2 ( 1 2 z s ) f 2 ( s , τ ) ) d s , Weierstrass-P-on-lattice 𝑧 𝕃 1 superscript 𝑧 2 8 superscript subscript 0 𝑠 superscript 𝑒 𝑠 2 1 2 𝑧 𝑠 subscript 𝑓 1 𝑠 𝜏 superscript 𝑒 𝑖 𝜏 𝑠 2 1 2 𝑧 𝑠 subscript 𝑓 2 𝑠 𝜏 𝑠 {\displaystyle{\displaystyle\wp\left(z\right)=\frac{1}{z^{2}}+8\int_{0}^{% \infty}s\left(e^{-s}{\sinh^{2}}\left(\tfrac{1}{2}zs\right)f_{1}(s,\tau)+e^{i% \tau s}{\sin^{2}}\left(\tfrac{1}{2}zs\right)f_{2}(s,\tau)\right)\mathrm{d}s,}}
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    DLMF:23.11.E2
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