DLMF:23.8.E4 (Q7286)

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DLMF:23.8.E4
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    Statements

    Defining formula
    ζ ⁡ ( z ) = η 1 ⁢ z ω 1 + π 2 ⁢ ω 1 ⁢ ∑ n = - ∞ ∞ cot ⁡ ( π ⁢ ( z + 2 ⁢ n ⁢ ω 3 ) 2 ⁢ ω 1 ) , Weierstrass-zeta-on-lattice 𝑧 𝕃 subscript 𝜂 1 𝑧 subscript 𝜔 1 𝜋 2 subscript 𝜔 1 superscript subscript 𝑛 𝜋 𝑧 2 𝑛 subscript 𝜔 3 2 subscript 𝜔 1 {\displaystyle{\displaystyle\zeta\left(z\right)=\frac{\eta_{1}z}{\omega_{1}}+% \frac{\pi}{2\omega_{1}}\sum_{n=-\infty}^{\infty}\cot\left(\frac{\pi(z+2n\omega% _{3})}{2\omega_{1}}\right),}}
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    DLMF id
    DLMF:23.8.E4
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