DLMF:22.15.E13 (Q7108): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
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.m3abdec

Revision as of 15:28, 2 January 2020

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DLMF:22.15.E13
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    Statements

    arccn ( x , k ) = x 1 d t ( 1 - t 2 ) ( k 2 + k 2 t 2 ) , inverse-Jacobi-elliptic-cn 𝑥 𝑘 superscript subscript 𝑥 1 𝑡 1 superscript 𝑡 2 superscript superscript 𝑘 2 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle\operatorname{arccn}\left(x,k\right)=\int_{x}^{1}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})({k^{\prime}}^{2}+k^{2}t^{2})}},}}
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    DLMF:22.15.E13
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    - 1 x 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1abdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3abdec
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