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DLMF:20.11.E8

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Formula:7544
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MaRDI QIDQ7544

  • Label: DLMF:20.11.E8


Digital Library of Mathematical Functions ID 20.11.E8

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


Constraint(s)

m , n = 2 , 3 , 4 formulae-sequence 𝑚 𝑛 2 3 4 {\displaystyle{\displaystyle m,n=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
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex
  • q 𝑞 {\displaystyle{\displaystyle q}} : nome
  •  Edit this on Wikidata

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