DLMF:20.7.E30 (Q6825): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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.m1odec

Latest revision as of 14:40, 2 January 2020

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DLMF:20.7.E30
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    Statements

    ( - i τ ) 1 / 2 θ 1 ( z | τ ) = - i exp ( i τ z 2 / π ) θ 1 ( z τ | τ ) , superscript 𝑖 𝜏 1 2 Jacobi-theta-tau 1 𝑧 𝜏 𝑖 𝑖 superscript 𝜏 superscript 𝑧 2 𝜋 Jacobi-theta-tau 1 𝑧 superscript 𝜏 superscript 𝜏 {\displaystyle{\displaystyle(-i\tau)^{1/2}\theta_{1}\left(z\middle|\tau\right)% =-i\exp\left(i\tau^{\prime}z^{2}/\pi\right)\theta_{1}\left(z\tau^{\prime}% \middle|\tau^{\prime}\right),}}
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    DLMF:20.7.E30
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    θ j ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    C20.S2.SS1.m1aodec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aidec
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    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2adec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2abdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C20.S1.XMD3.m1zdec
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    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    C20.S1.XMD4.m1odec
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