DLMF:22.9.E7 (Q6999): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11600 / rank
 
Normal rank
Property / Symbols used: Q11600 / qualifier
 
Defining formula:

K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

\compellintKk@{\NVar{k}}
Property / Symbols used: Q11600 / qualifier
 
xml-id: C19.S2.E8.m1afdec
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.m1fdec
Property / Symbols used
 
Property / Symbols used: Q12002 / rank
 
Normal rank
Property / Symbols used: Q12002 / qualifier
 
Defining formula:

κ 𝜅 {\displaystyle{\displaystyle\kappa}}

\kappa
Property / Symbols used: Q12002 / qualifier
 
xml-id: C22.S9.XMD6.m1dec

Latest revision as of 15:07, 2 January 2020

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DLMF:22.9.E7
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    Statements

    κ = dn ( 2 K ( k ) / 3 , k ) , 𝜅 Jacobi-elliptic-dn 2 complete-elliptic-integral-first-kind-K 𝑘 3 𝑘 {\displaystyle{\displaystyle\kappa=\operatorname{dn}\left(2K\left(k\right)/3,k% \right),}}
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    DLMF:22.9.E7
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    dn ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E6.m2abdec
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    K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    C19.S2.E8.m1afdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1fdec
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    κ 𝜅 {\displaystyle{\displaystyle\kappa}}
    C22.S9.XMD6.m1dec
    0 references