DLMF:22.15.E11 (Q7106): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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.m1jdec

Latest revision as of 15:28, 2 January 2020

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DLMF:22.15.E11
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    Statements

    x = 0 sn ( x , k ) d t ( 1 - t 2 ) ( 1 - k 2 t 2 ) , 𝑥 superscript subscript 0 Jacobi-elliptic-sn 𝑥 𝑘 𝑡 1 superscript 𝑡 2 1 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle x=\int_{0}^{\operatorname{sn}\left(x,k\right)}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}},}}
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    DLMF:22.15.E11
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    0 k 1 0 𝑘 1 {\displaystyle{\displaystyle 0\leq k\leq 1}}
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    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2aadec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C22.S1.XMD1.m1jdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1jdec
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