DLMF:20.5.E10 (Q6777)

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DLMF:20.5.E10
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    Defining formula
    θ 1 ′ ⁡ ( z , q ) θ 1 ⁡ ( z , q ) - cot ⁡ z = 4 ⁢ sin ⁡ ( 2 ⁢ z ) ⁢ ∑ n = 1 ∞ q 2 ⁢ n 1 - 2 ⁢ q 2 ⁢ n ⁢ cos ⁡ ( 2 ⁢ z ) + q 4 ⁢ n = 4 ⁢ ∑ n = 1 ∞ q 2 ⁢ n 1 - q 2 ⁢ n ⁢ sin ⁡ ( 2 ⁢ n ⁢ z ) , diffop Jacobi-theta 1 1 𝑧 𝑞 Jacobi-theta 1 𝑧 𝑞 𝑧 4 2 𝑧 superscript subscript 𝑛 1 superscript 𝑞 2 𝑛 1 2 superscript 𝑞 2 𝑛 2 𝑧 superscript 𝑞 4 𝑛 4 superscript subscript 𝑛 1 superscript 𝑞 2 𝑛 1 superscript 𝑞 2 𝑛 2 𝑛 𝑧 {\displaystyle{\displaystyle\frac{\theta_{1}'\left(z,q\right)}{\theta_{1}\left% (z,q\right)}-\cot z=4\sin\left(2z\right)\sum_{n=1}^{\infty}\frac{q^{2n}}{1-2q^% {2n}\cos\left(2z\right)+q^{4n}}=4\sum_{n=1}^{\infty}\frac{q^{2n}}{1-q^{2n}}% \sin\left(2nz\right),}}
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    DLMF id
    DLMF:20.5.E10
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