DLMF:20.7.E30 (Q6825): 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.m1odec

Latest revision as of 14:40, 2 January 2020

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DLMF:20.7.E30
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    Statements

    Defining formula
    ( - 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),}}
    0 references
    DLMF id
    DLMF:20.7.E30
    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.m1aodec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1zdec
    0 references
    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1odec
    0 references
     
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