DLMF:23.6.E15 (Q7256)

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DLMF:23.6.E15
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    Statements

    Defining formula
    σ ⁡ ( u + ω j ) σ ⁡ ( ω j ) = exp ⁡ ( η j ⁢ u + η j ⁢ u 2 2 ⁢ ω 1 ) ⁢ θ j + 1 ⁡ ( z , q ) θ j + 1 ⁡ ( 0 , q ) , Weierstrass-sigma-on-lattice 𝑢 subscript 𝜔 𝑗 𝕃 Weierstrass-sigma-on-lattice subscript 𝜔 𝑗 𝕃 subscript 𝜂 𝑗 𝑢 subscript 𝜂 𝑗 superscript 𝑢 2 2 subscript 𝜔 1 Jacobi-theta 𝑗 1 𝑧 𝑞 Jacobi-theta 𝑗 1 0 𝑞 {\displaystyle{\displaystyle\frac{\sigma\left(u+\omega_{j}\right)}{\sigma\left% (\omega_{j}\right)}=\exp\left(\eta_{j}u+\frac{\eta_{j}u^{2}}{2\omega_{1}}% \right)\frac{\theta_{j+1}\left(z,q\right)}{\theta_{j+1}\left(0,q\right)},}}
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    DLMF id
    DLMF:23.6.E15
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    constraint
    j = 1 , 2 , 3 𝑗 1 2 3 {\displaystyle{\displaystyle j=1,2,3}}
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