DLMF:22.16.E1 (Q7120): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10812 / rank
 
Normal rank
Property / Symbols used: Q10812 / qualifier
 
Defining formula:

ℝ {\displaystyle{\displaystyle\mathbb{R}}}

\Reals
Property / Symbols used: Q10812 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r14.m2adec

Revision as of 15:30, 2 January 2020

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DLMF:22.16.E1
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    Statements

    Defining formula
    am ⁡ ( x , k ) = Arcsin ⁡ ( sn ⁡ ( x , k ) ) , Jacobi-elliptic-amplitude 𝑥 𝑘 multivalued-inverse-sine Jacobi-elliptic-sn 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{am}\left(x,k\right)=\operatorname{% Arcsin}\left(\operatorname{sn}\left(x,k\right)\right),}}
    0 references
    DLMF id
    DLMF:22.16.E1
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    constraint
    x ∈ ℝ 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
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    Symbols used
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2adec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
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    general arcsine function
    Defining formula
    Arcsin ⁡ z multivalued-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsin}\NVar{z}}}
    xml-id
    C4.S23.E1.m2adec
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    Q10812
    Defining formula
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2adec
    0 references
     
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