DLMF:20.7.E27 (Q6822): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11949 / rank
 
Normal rank
Property / Symbols used: Q11949 / qualifier
 
Defining formula:

τ 𝜏 {\displaystyle{\displaystyle\tau}}

\tau
Property / Symbols used: Q11949 / qualifier
 
xml-id: C20.S1.XMD4.m1ldec

Latest revision as of 14:40, 2 January 2020

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DLMF:20.7.E27
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    Statements

    Defining formula
    θ 2 ⁡ ( z | τ + 1 ) = e i ⁢ π / 4 ⁢ θ 2 ⁡ ( z | τ ) , Jacobi-theta-tau 2 𝑧 𝜏 1 superscript 𝑒 𝑖 𝜋 4 Jacobi-theta-tau 2 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{2}\left(z\middle|\tau+1\right)=e^{i\pi/4}% \theta_{2}\left(z\middle|\tau\right),}}
    0 references
    DLMF id
    DLMF:20.7.E27
    0 references
    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.m1aldec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1wdec
    0 references
    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1ldec
    0 references
     
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