DLMF:20.7.E34 (Q6829)

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DLMF:20.7.E34
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    Statements

    Defining formula
    θ 1 ⁡ ( z , q 2 ) ⁢ θ 3 ⁡ ( z , q 2 ) θ 1 ⁡ ( z , i ⁢ q ) = θ 2 ⁡ ( z , q 2 ) ⁢ θ 4 ⁡ ( z , q 2 ) θ 2 ⁡ ( z , i ⁢ q ) = i - 1 / 4 ⁢ θ 2 ⁡ ( 0 , q 2 ) ⁢ θ 4 ⁡ ( 0 , q 2 ) 2 . Jacobi-theta 1 𝑧 superscript 𝑞 2 Jacobi-theta 3 𝑧 superscript 𝑞 2 Jacobi-theta 1 𝑧 𝑖 𝑞 Jacobi-theta 2 𝑧 superscript 𝑞 2 Jacobi-theta 4 𝑧 superscript 𝑞 2 Jacobi-theta 2 𝑧 𝑖 𝑞 superscript 𝑖 1 4 Jacobi-theta 2 0 superscript 𝑞 2 Jacobi-theta 4 0 superscript 𝑞 2 2 {\displaystyle{\displaystyle\frac{\theta_{1}\left(z,q^{2}\right)\theta_{3}% \left(z,q^{2}\right)}{\theta_{1}\left(z,iq\right)}=\frac{\theta_{2}\left(z,q^{% 2}\right)\theta_{4}\left(z,q^{2}\right)}{\theta_{2}\left(z,iq\right)}=i^{-1/4}% \sqrt{\frac{\theta_{2}\left(0,q^{2}\right)\theta_{4}\left(0,q^{2}\right)}{2}}.}}
    0 references
    DLMF id
    DLMF:20.7.E34
    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.m2andec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
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    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1addec
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