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Formula:7937

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Digital Library of Mathematical Functions ID 23.6.E3

e 2 ⁡ = π 2 12 ⁢ ω 1 2 ⁢ ( θ 2 4 ⁡ ( 0 , q ) - θ 4 4 ⁡ ( 0 , q ) ) , Weierstrass-e-on-lattice 2 𝕃 superscript 𝜋 2 12 superscript subscript 𝜔 1 2 Jacobi-theta 2 4 0 𝑞 Jacobi-theta 4 4 0 𝑞 {\displaystyle{\displaystyle e_{2}=\frac{\pi^{2}}{12\omega_{1}^{2}}\left({% \theta_{2}^{4}}\left(0,q\right)-{\theta_{4}^{4}}\left(0,q\right)\right),}}


Constraint(s)

Symbols List

  • θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}} :
  • e j ⁡ Weierstrass-e-on-lattice 𝑗 𝕃 {\displaystyle{\displaystyle e_{\NVar{j}}}} :
  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • 𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}} : lattice
  • q 𝑞 {\displaystyle{\displaystyle q}} : nome
  • ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}} : lattice generators
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:02.
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