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Formula:7622

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Digital Library of Mathematical Functions ID 22.2.E7

sd ⁡ ( z , k ) = θ 3 2 ⁡ ( 0 , q ) θ 2 ⁡ ( 0 , q ) ⁢ θ 4 ⁡ ( 0 , q ) ⁢ θ 1 ⁡ ( ζ , q ) θ 3 ⁡ ( ζ , q ) = 1 ds ⁡ ( z , k ) , Jacobi-elliptic-sd 𝑧 𝑘 Jacobi-theta 3 2 0 𝑞 Jacobi-theta 2 0 𝑞 Jacobi-theta 4 0 𝑞 Jacobi-theta 1 𝜁 𝑞 Jacobi-theta 3 𝜁 𝑞 1 Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(z,k\right)=\frac{{\theta_{3% }^{2}}\left(0,q\right)}{\theta_{2}\left(0,q\right)\theta_{4}\left(0,q\right)}% \frac{\theta_{1}\left(\zeta,q\right)}{\theta_{3}\left(\zeta,q\right)}=\frac{1}% {\operatorname{ds}\left(z,k\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)}} :
  • q 𝑞 {\displaystyle{\displaystyle q}} : nome
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex
  • k 𝑘 {\displaystyle{\displaystyle k}} : modulus
  • ζ 𝜁 {\displaystyle{\displaystyle\zeta}} : change of variable
  •  Edit this on Wikidata

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