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DLMF:23.6.E34

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Formula:7970
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MaRDI QIDQ7970

  • Label: DLMF:23.6.E34


Digital Library of Mathematical Functions ID 23.6.E34

2 ⁢ ω 1 = ∫ e 1 ⁡ ∞ d u ( u - e 1 ⁡ ) ⁢ ( u - e 2 ⁡ ) ⁢ ( u - e 3 ⁡ ) = ∫ e 3 ⁡ e 2 ⁡ d u ( e 1 ⁡ - u ) ⁢ ( e 2 ⁡ - u ) ⁢ ( u - e 3 ⁡ ) , 2 subscript 𝜔 1 superscript subscript Weierstrass-e-on-lattice 1 𝕃 𝑢 𝑢 Weierstrass-e-on-lattice 1 𝕃 𝑢 Weierstrass-e-on-lattice 2 𝕃 𝑢 Weierstrass-e-on-lattice 3 𝕃 superscript subscript Weierstrass-e-on-lattice 3 𝕃 Weierstrass-e-on-lattice 2 𝕃 𝑢 Weierstrass-e-on-lattice 1 𝕃 𝑢 Weierstrass-e-on-lattice 2 𝕃 𝑢 𝑢 Weierstrass-e-on-lattice 3 𝕃 {\displaystyle{\displaystyle 2\omega_{1}=\int_{e_{1}}^{\infty}\frac{\mathrm{d}% u}{\sqrt{(u-e_{1})(u-e_{2})(u-e_{3})}}=\int_{e_{3}}^{e_{2}}\frac{\mathrm{d}u}{% \sqrt{(e_{1}-u)(e_{2}-u)(u-e_{3})}},}}


Constraint(s)

Symbols List

  • e j ⁡ Weierstrass-e-on-lattice 𝑗 𝕃 {\displaystyle{\displaystyle e_{\NVar{j}}}} :
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • 𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}} : lattice
  • ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}} : lattice generators
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