DLMF:20.6.E5 (Q6789): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: coefficient (locally) / rank
 
Normal rank
Property / Symbols used: coefficient (locally) / qualifier
 
Defining formula:

γ 2 ⁢ j ⁢ ( τ ) subscript 𝛾 2 𝑗 𝜏 {\displaystyle{\displaystyle\gamma_{2j}(\tau)}}

\gamma_{2j}(\tau)
Property / Symbols used: coefficient (locally) / qualifier
 
xml-id: C20.S6.XMD4.m1dec

Latest revision as of 14:36, 2 January 2020

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DLMF:20.6.E5
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    Statements

    Defining formula
    θ 4 ⁡ ( π ⁢ z | τ ) = θ 4 ⁡ ( 0 | τ ) ⁢ exp ⁡ ( - ∑ j = 1 ∞ 1 2 ⁢ j ⁢ γ 2 ⁢ j ⁢ ( τ ) ⁢ z 2 ⁢ j ) . Jacobi-theta-tau 4 𝜋 𝑧 𝜏 Jacobi-theta-tau 4 0 𝜏 superscript subscript 𝑗 1 1 2 𝑗 subscript 𝛾 2 𝑗 𝜏 superscript 𝑧 2 𝑗 {\displaystyle{\displaystyle\theta_{4}\left(\pi z\middle|\tau\right)=\theta_{4% }\left(0\middle|\tau\right)\exp\left(-\sum_{j=1}^{\infty}\frac{1}{2j}\gamma_{2% j}(\tau)z^{2j}\right).}}
    0 references
    DLMF id
    DLMF:20.6.E5
    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.m1acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2acdec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1ddec
    0 references
    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1cdec
    0 references
    coefficient (locally)
    Defining formula
    γ 2 ⁢ j ⁢ ( τ ) subscript 𝛾 2 𝑗 𝜏 {\displaystyle{\displaystyle\gamma_{2j}(\tau)}}
    xml-id
    C20.S6.XMD4.m1dec
    0 references
     
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