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

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2addec
Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
Defining formula:

exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11948 / rank
 
Normal rank
Property / Symbols used: Q11948 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11948 / qualifier
 
xml-id: C20.S1.XMD3.m1ddec
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.m1cdec
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

    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:20.6.E5
    0 references
    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.m1acdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
    0 references
    exp z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    C4.S2.E19.m2acdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C20.S1.XMD3.m1ddec
    0 references
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    C20.S1.XMD4.m1cdec
    0 references
    γ 2 j ( τ ) subscript 𝛾 2 𝑗 𝜏 {\displaystyle{\displaystyle\gamma_{2j}(\tau)}}
    C20.S6.XMD4.m1dec
    0 references