DLMF:20.2.E3 (Q6743)

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DLMF:20.2.E3
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    Statements

    Defining formula
    θ 3 ⁡ ( z | τ ) = θ 3 ⁡ ( z , q ) = 1 + 2 ⁢ ∑ n = 1 ∞ q n 2 ⁢ cos ⁡ ( 2 ⁢ n ⁢ z ) , Jacobi-theta-tau 3 𝑧 𝜏 Jacobi-theta 3 𝑧 𝑞 1 2 superscript subscript 𝑛 1 superscript 𝑞 superscript 𝑛 2 2 𝑛 𝑧 {\displaystyle{\displaystyle\theta_{3}\left(z\middle|\tau\right)=\theta_{3}% \left(z,q\right)=1+2\sum\limits_{n=1}^{\infty}q^{n^{2}}\cos\left(2nz\right),}}
    0 references
    DLMF id
    DLMF:20.2.E3
    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.m2abdec
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    Q11946
    Defining formula
    θ j ⁡ ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    xml-id
    C20.S2.SS1.m1abdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1bdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1bdec
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    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1bdec
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    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1bdec
    0 references
     
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