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Formula:8062

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Digital Library of Mathematical Functions ID 23.19.E2

J ⁡ ( τ ) = 4 27 ⁢ ( 1 - λ ⁡ ( τ ) + λ 2 ⁡ ( τ ) ) 3 ( λ ⁡ ( τ ) ⁢ ( 1 - λ ⁡ ( τ ) ) ) 2 , Kleins-invariant-modular-J 𝜏 4 27 superscript 1 modular-Lambda 𝜏 modular-Lambda 2 𝜏 3 superscript modular-Lambda 𝜏 1 modular-Lambda 𝜏 2 {\displaystyle{\displaystyle J\left(\tau\right)=\frac{4}{27}\frac{\left(1-% \lambda\left(\tau\right)+{\lambda^{2}}\left(\tau\right)\right)^{3}}{\left(% \lambda\left(\tau\right)\left(1-\lambda\left(\tau\right)\right)\right)^{2}},}}


Constraint(s)

Symbols List

  • J ⁡ ( τ ) Kleins-invariant-modular-J 𝜏 {\displaystyle{\displaystyle J\left(\NVar{\tau}\right)}} : Klein’s complete invariant
  • λ ⁡ ( τ ) modular-Lambda 𝜏 {\displaystyle{\displaystyle\lambda\left(\NVar{\tau}\right)}} : elliptic modular function
  • τ 𝜏 {\displaystyle{\displaystyle\tau}} : complex variable
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