DLMF:20.5.E8 (Q6775): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11947 / rank
 
Normal rank
Property / Symbols used: Q11947 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11947 / qualifier
 
xml-id: C20.S1.XMD2.m1gdec
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.m1gdec
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

Latest revision as of 14:33, 2 January 2020

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DLMF:20.5.E8
No description defined

    Statements

    θ 4 ( z | τ ) = θ 4 ( 0 | τ ) n = 1 sin ( ( n - 1 2 ) π τ + z ) sin ( ( n - 1 2 ) π τ - z ) sin 2 ( ( n - 1 2 ) π τ ) . Jacobi-theta-tau 4 𝑧 𝜏 Jacobi-theta-tau 4 0 𝜏 superscript subscript product 𝑛 1 𝑛 1 2 𝜋 𝜏 𝑧 𝑛 1 2 𝜋 𝜏 𝑧 2 𝑛 1 2 𝜋 𝜏 {\displaystyle{\displaystyle\theta_{4}\left(z\middle|\tau\right)=\theta_{4}% \left(0\middle|\tau\right)\prod_{n=1}^{\infty}\frac{\sin\left((n-\tfrac{1}{2})% \pi\tau+z\right)\sin\left((n-\tfrac{1}{2})\pi\tau-z\right)}{{\sin^{2}}\left((n% -\tfrac{1}{2})\pi\tau\right)}.}}
    0 references
    DLMF:20.5.E8
    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.m2acdec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2abdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C20.S1.XMD2.m1gdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C20.S1.XMD3.m1gdec
    0 references
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    C20.S1.XMD4.m1cdec
    0 references