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DLMF:20.11.E6

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Formula:7542
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MaRDI QIDQ7542

  • Label: DLMF:20.11.E6


Digital Library of Mathematical Functions ID 20.11.E6

φ m , 1 ⁡ ( z , q ) = θ 1 ′ ⁡ ( 0 , q ) ⁢ θ m ⁡ ( z , q ) θ m ⁡ ( 0 , q ) ⁢ θ 1 ⁡ ( z , q ) , Jacobi-theta-combined 𝑚 1 𝑧 𝑞 diffop Jacobi-theta 1 1 0 𝑞 Jacobi-theta 𝑚 𝑧 𝑞 Jacobi-theta 𝑚 0 𝑞 Jacobi-theta 1 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{m,1}\left(z,q\right)=\frac{\theta_{1}'% \left(0,q\right)\theta_{m}\left(z,q\right)}{\theta_{m}\left(0,q\right)\theta_{% 1}\left(z,q\right)},}}


Constraint(s)

m = 2 , 3 , 4 𝑚 2 3 4 {\displaystyle{\displaystyle m=2,3,4}}

Symbols List

  • θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}} :
  • φ n , m ⁡ ( z , q ) Jacobi-theta-combined 𝑛 𝑚 𝑧 𝑞 {\displaystyle{\displaystyle\varphi_{\NVar{n},\NVar{m}}\left(\NVar{z},\NVar{q}% \right)}} :
  • m 𝑚 {\displaystyle{\displaystyle m}} : integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex
  • q 𝑞 {\displaystyle{\displaystyle q}} : nome
  •  Edit this on Wikidata

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