DLMF:20.5.E1 (Q6768)

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DLMF:20.5.E1
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    Statements

    Defining formula
    θ 1 ⁡ ( z , q ) = 2 ⁢ q 1 / 4 ⁢ sin ⁡ z ⁢ ∏ n = 1 ∞ ( 1 - q 2 ⁢ n ) ⁢ ( 1 - 2 ⁢ q 2 ⁢ n ⁢ cos ⁡ ( 2 ⁢ z ) + q 4 ⁢ n ) , Jacobi-theta 1 𝑧 𝑞 2 superscript 𝑞 1 4 𝑧 superscript subscript product 𝑛 1 1 superscript 𝑞 2 𝑛 1 2 superscript 𝑞 2 𝑛 2 𝑧 superscript 𝑞 4 𝑛 {\displaystyle{\displaystyle\theta_{1}\left(z,q\right)=2q^{1/4}\sin z\prod% \limits_{n=1}^{\infty}{\left(1-q^{2n}\right)}{\left(1-2q^{2n}\cos\left(2z% \right)+q^{4n}\right)},}}
    0 references
    DLMF id
    DLMF:20.5.E1
    0 references
    Symbols used
    Q11945
    Defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2adec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1dec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1dec
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    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1dec
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