DLMF:22.16.E17 (Q7137): 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: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec
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.m1pdec
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.m1ndec

Latest revision as of 15:33, 2 January 2020

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DLMF:22.16.E17
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    Statements

    ( x , k ) = 0 x dn 2 ( t , k ) d t . Jacobi-Epsilon 𝑥 𝑘 superscript subscript 0 𝑥 Jacobi-elliptic-dn 2 𝑡 𝑘 𝑡 {\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=\int_{0}^{x}{% \operatorname{dn}^{2}}\left(t,k\right)\mathrm{d}t.}}
    0 references
    DLMF:22.16.E17
    0 references
    ( x , k ) Jacobi-Epsilon 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}
    C22.S16.E14.m2acdec
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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.m2aadec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1addec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3addec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C22.S1.XMD1.m1pdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1ndec
    0 references