DLMF:29.2.E5 (Q8578): Difference between revisions

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Changed an Item: Wikidata Toolkit example test statement addition
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Jacobi’s amplitude function / rank
 
Normal rank
Property / Symbols used: Jacobi’s amplitude function / qualifier
 
Defining formula:

am ( x , k ) Jacobi-elliptic-amplitude 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}

\Jacobiamk@{\NVar{x}}{\NVar{k}}
Property / Symbols used: Jacobi’s amplitude function / qualifier
 
xml-id: C22.S16.E1.m2adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q12348 / rank
 
Normal rank
Property / Symbols used: Q12348 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12348 / qualifier
 
xml-id: C29.S1.XMD6.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12350 / rank
 
Normal rank
Property / Symbols used: Q12350 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12350 / qualifier
 
xml-id: C29.S1.XMD8.m1edec

Latest revision as of 15:42, 2 January 2020

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DLMF:29.2.E5
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    Statements

    ϕ = 1 2 π - am ( z , k ) . italic-ϕ 1 2 𝜋 Jacobi-elliptic-amplitude 𝑧 𝑘 {\displaystyle{\displaystyle\phi=\tfrac{1}{2}\pi-\operatorname{am}\left(z,k% \right).}}
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    DLMF:29.2.E5
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    am ( x , k ) Jacobi-elliptic-amplitude 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}
    C22.S16.E1.m2adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C29.S1.XMD6.m1cdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C29.S1.XMD8.m1edec
    0 references