DLMF:23.8.E4 (Q7286): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cotangent function / rank
 
Normal rank
Property / Symbols used: cotangent function / qualifier
 
Defining formula:

cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}

\cot@@{\NVar{z}}
Property / Symbols used: cotangent function / qualifier
 
xml-id: C4.S14.E7.m2aadec
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.m1cdec
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.m1cdec
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.m1cdec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12072 / rank
 
Normal rank
Property / Symbols used: Q12072 / qualifier
 
Defining formula:

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

\eta_{j}
Property / Symbols used: Q12072 / qualifier
 
xml-id: C23.S8.XMD1.m1adec

Latest revision as of 15:56, 2 January 2020

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DLMF:23.8.E4
No description defined

    Statements

    Defining formula
    ζ ⁡ ( z ) = η 1 ⁢ z ω 1 + π 2 ⁢ ω 1 ⁢ ∑ n = - ∞ ∞ cot ⁡ ( π ⁢ ( z + 2 ⁢ n ⁢ ω 3 ) 2 ⁢ ω 1 ) , Weierstrass-zeta-on-lattice 𝑧 𝕃 subscript 𝜂 1 𝑧 subscript 𝜔 1 𝜋 2 subscript 𝜔 1 superscript subscript 𝑛 𝜋 𝑧 2 𝑛 subscript 𝜔 3 2 subscript 𝜔 1 {\displaystyle{\displaystyle\zeta\left(z\right)=\frac{\eta_{1}z}{\omega_{1}}+% \frac{\pi}{2\omega_{1}}\sum_{n=-\infty}^{\infty}\cot\left(\frac{\pi(z+2n\omega% _{3})}{2\omega_{1}}\right),}}
    0 references
    DLMF id
    DLMF:23.8.E4
    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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2aadec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1cdec
    0 references
    Q12060
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C23.S1.XMD3.m1cdec
    0 references
    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1cdec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1cdec
    0 references
    Q12072
    Defining formula
    η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}
    xml-id
    C23.S8.XMD1.m1adec
    0 references
     
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