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Formula:7929

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Digital Library of Mathematical Functions ID 23.5.E7

e 1 ⁡ = e 2 ⁢ π ⁢ i / 3 ⁢ e 3 ⁡ = e - 2 ⁢ π ⁢ i / 3 ⁢ e 2 ⁡ = ( Γ ⁡ ( 1 3 ) ) 6 2 14 / 3 ⁢ π 2 ⁢ ω 1 2 , Weierstrass-e-on-lattice 1 𝕃 superscript 𝑒 2 𝜋 𝑖 3 Weierstrass-e-on-lattice 3 𝕃 superscript 𝑒 2 𝜋 𝑖 3 Weierstrass-e-on-lattice 2 𝕃 superscript Euler-Gamma 1 3 6 superscript 2 14 3 superscript 𝜋 2 superscript subscript 𝜔 1 2 {\displaystyle{\displaystyle e_{1}=e^{2\pi i/3}e_{3}=e^{-2\pi i/3}e_{2}=\frac{% \left(\Gamma\left(\tfrac{1}{3}\right)\right)^{6}}{2^{14/3}\pi^{2}\omega_{1}^{2% }},}}


Constraint(s)

Symbols List

  • Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}} : gamma function
  • 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
  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}} : imaginary unit
  • 𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}} : lattice
  • 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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