DLMF:23.10.E12 (Q7310): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: DLMF:23.2.E5 / rank
 
Normal rank
Property / Symbols used: DLMF:23.2.E5 / qualifier
 
Defining formula:

ζ ⁡ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}

\Weierstrasszetalatt@@{\NVar{z}}{\NVar{\mathbb{L}}}
Property / Symbols used: DLMF:23.2.E5 / qualifier
 
xml-id: C23.S2.E5.m2acdec
Property / Symbols used
 
Property / Symbols used: Q12055 / rank
 
Normal rank
Property / Symbols used: Q12055 / qualifier
 
Defining formula:

𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}

\mathbb{L}
Property / Symbols used: Q12055 / qualifier
 
xml-id: C23.S1.XMD1.m1kdec
Property / Symbols used
 
Property / Symbols used: Q12060 / rank
 
Normal rank
Property / Symbols used: Q12060 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12060 / qualifier
 
xml-id: C23.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q12056 / rank
 
Normal rank
Property / Symbols used: Q12056 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12056 / qualifier
 
xml-id: C23.S1.XMD7.m1edec
Property / Symbols used
 
Property / Symbols used: Q12049 / rank
 
Normal rank
Property / Symbols used: Q12049 / qualifier
 
Defining formula:

ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}

\omega_{1}
Property / Symbols used: Q12049 / qualifier
 
xml-id: C23.S1.XMD8.m1adec
Property / Symbols used
 
Property / Symbols used: Q12059 / rank
 
Normal rank
Property / Symbols used: Q12059 / qualifier
 
Defining formula:

η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}

\eta_{j}
Property / Symbols used: Q12059 / qualifier
 
xml-id: C23.S2.XMD6.m1dec

Latest revision as of 15:59, 2 January 2020

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DLMF:23.10.E12
No description defined

    Statements

    Defining formula
    n ⁢ ζ ⁡ ( n ⁢ z ) = - n ⁢ ( n - 1 ) ⁢ ( η 1 + η 3 ) + ∑ j = 0 n - 1 ∑ ℓ = 0 n - 1 ζ ⁡ ( z + 2 ⁢ j n ⁢ ω 1 + 2 ⁢ ℓ n ⁢ ω 3 ) , 𝑛 Weierstrass-zeta-on-lattice 𝑛 𝑧 𝕃 𝑛 𝑛 1 subscript 𝜂 1 subscript 𝜂 3 superscript subscript 𝑗 0 𝑛 1 superscript subscript ℓ 0 𝑛 1 Weierstrass-zeta-on-lattice 𝑧 2 𝑗 𝑛 subscript 𝜔 1 2 ℓ 𝑛 subscript 𝜔 3 𝕃 {\displaystyle{\displaystyle n\zeta\left(nz\right)=-n(n-1)(\eta_{1}+\eta_{3})+% \sum_{j=0}^{n-1}\sum_{\ell=0}^{n-1}\zeta\left(z+\frac{2j}{n}\omega_{1}+\frac{2% \ell}{n}\omega_{3}\right),}}
    0 references
    DLMF id
    DLMF:23.10.E12
    0 references
    Symbols used
    DLMF:23.2.E5
    Defining formula
    ζ ⁡ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E5.m2acdec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1kdec
    0 references
    Q12060
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C23.S1.XMD3.m1adec
    0 references
    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1edec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1adec
    0 references
    Q12059
    Defining formula
    η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}
    xml-id
    C23.S2.XMD6.m1dec
    0 references
     
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