DLMF:20.2.E9 (Q6749)

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DLMF:20.2.E9
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    Statements

    Defining formula
    θ 4 ⁡ ( z + ( m + n ⁢ τ ) ⁢ π | τ ) = ( - 1 ) n ⁢ q - n 2 ⁢ e - 2 ⁢ i ⁢ n ⁢ z ⁢ θ 4 ⁡ ( z | τ ) . Jacobi-theta-tau 4 𝑧 𝑚 𝑛 𝜏 𝜋 𝜏 superscript 1 𝑛 superscript 𝑞 superscript 𝑛 2 superscript 𝑒 2 𝑖 𝑛 𝑧 Jacobi-theta-tau 4 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{4}\left(z+(m+n\tau)\pi\middle|\tau\right)=% (-1)^{n}q^{-n^{2}}e^{-2inz}\theta_{4}\left(z\middle|\tau\right).}}
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    DLMF id
    DLMF:20.2.E9
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    Symbols used
    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.m1agdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    Q11951
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C20.S1.XMD1.m1ddec
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    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1hdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1hdec
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    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1hdec
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    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1gdec
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