DLMF:20.2.E2 (Q6742)

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DLMF:20.2.E2
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    Statements

    Defining formula
    θ 2 ⁡ ( z | τ ) = θ 2 ⁡ ( z , q ) = 2 ⁢ ∑ n = 0 ∞ q ( n + 1 2 ) 2 ⁢ cos ⁡ ( ( 2 ⁢ n + 1 ) ⁢ z ) , Jacobi-theta-tau 2 𝑧 𝜏 Jacobi-theta 2 𝑧 𝑞 2 superscript subscript 𝑛 0 superscript 𝑞 superscript 𝑛 1 2 2 2 𝑛 1 𝑧 {\displaystyle{\displaystyle\theta_{2}\left(z\middle|\tau\right)=\theta_{2}% \left(z,q\right)=2\sum\limits_{n=0}^{\infty}q^{(n+\frac{1}{2})^{2}}\cos\left((% 2n+1)z\right),}}
    0 references
    DLMF id
    DLMF:20.2.E2
    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.m2aadec
    0 references
    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.m1aadec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1adec
    0 references
     
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