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

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Changed an Item: Add constraint
 
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Property / constraint
 

x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}

x\in\Reals
Property / constraint: x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellsnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E4.m2adec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec
Property / Symbols used
 
Property / Symbols used: general arcsine function / rank
 
Normal rank
Property / Symbols used: general arcsine function / qualifier
 
Defining formula:

Arcsin z multivalued-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsin}\NVar{z}}}

\Asin@@{\NVar{z}}
Property / Symbols used: general arcsine function / qualifier
 
xml-id: C4.S23.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10812 / rank
 
Normal rank
Property / Symbols used: Q10812 / qualifier
 
Defining formula:

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

\Reals
Property / Symbols used: Q10812 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r14.m2adec
Property / Symbols used
 
Property / Symbols used: Q12003 / rank
 
Normal rank
Property / Symbols used: Q12003 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12003 / qualifier
 
xml-id: C22.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1dec

Latest revision as of 15:30, 2 January 2020

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DLMF:22.16.E1
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    Statements

    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:22.16.E1
    0 references
    x 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
    0 references
    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2adec
    0 references
    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    Arcsin z multivalued-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsin}\NVar{z}}}
    C4.S23.E1.m2adec
    0 references
    {\displaystyle{\displaystyle\mathbb{R}}}
    introduction.Sx4.p2.t1.r14.m2adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C22.S1.XMD1.m1dec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1dec
    0 references