DLMF:23.8.E5 (Q7287): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
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: cosecant function / rank
 
Normal rank
Property / Symbols used: cosecant function / qualifier
 
Defining formula:

csc z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}

\csc@@{\NVar{z}}
Property / Symbols used: cosecant function / qualifier
 
xml-id: C4.S14.E5.m2abdec
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.m1ddec
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.m1ddec
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.m1bdec

Latest revision as of 15:56, 2 January 2020

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DLMF:23.8.E5
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    Statements

    η 1 = π 2 2 ω 1 ( 1 6 + n = 1 csc 2 ( n π ω 3 ω 1 ) ) , subscript 𝜂 1 superscript 𝜋 2 2 subscript 𝜔 1 1 6 superscript subscript 𝑛 1 2 𝑛 𝜋 subscript 𝜔 3 subscript 𝜔 1 {\displaystyle{\displaystyle\eta_{1}=\frac{\pi^{2}}{2\omega_{1}}\left(\frac{1}% {6}+\sum_{n=1}^{\infty}{\csc^{2}}\left(\frac{n\pi\omega_{3}}{\omega_{1}}\right% )\right),}}
    0 references
    DLMF:23.8.E5
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
    0 references
    csc z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    C4.S14.E5.m2abdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C23.S1.XMD3.m1ddec
    0 references
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    C23.S1.XMD8.m1ddec
    0 references
    η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}
    C23.S8.XMD1.m1bdec
    0 references