DLMF:20.2.E1 (Q6741)

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DLMF:20.2.E1
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    Statements

    Defining formula
    θ 1 ⁡ ( z | τ ) = θ 1 ⁡ ( z , q ) = 2 ⁢ ∑ n = 0 ∞ ( - 1 ) n ⁢ q ( n + 1 2 ) 2 ⁢ sin ⁡ ( ( 2 ⁢ n + 1 ) ⁢ z ) , Jacobi-theta-tau 1 𝑧 𝜏 Jacobi-theta 1 𝑧 𝑞 2 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 𝑞 superscript 𝑛 1 2 2 2 𝑛 1 𝑧 {\displaystyle{\displaystyle\theta_{1}\left(z\middle|\tau\right)=\theta_{1}% \left(z,q\right)=2\sum\limits_{n=0}^{\infty}(-1)^{n}q^{(n+\frac{1}{2})^{2}}% \sin\left((2n+1)z\right),}}
    0 references
    DLMF id
    DLMF:20.2.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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    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.m1adec
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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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    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1dec
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    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1dec
    0 references
     
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