DLMF:22.15.E16 (Q7111): Difference between revisions

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Property / constraint
 

- 1 / k x 1 / k 1 superscript 𝑘 𝑥 1 superscript 𝑘 {\displaystyle{\displaystyle-1/k^{\prime}\leq x\leq 1/k^{\prime}}}

-1/k^{\prime}\leq x\leq 1/k^{\prime}
Property / constraint: - 1 / k x 1 / k 1 superscript 𝑘 𝑥 1 superscript 𝑘 {\displaystyle{\displaystyle-1/k^{\prime}\leq x\leq 1/k^{\prime}}} / rank
 
Normal rank

Revision as of 17:10, 30 December 2019

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DLMF:22.15.E16
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    Statements

    arcsd ( x , k ) = 0 x d t ( 1 - k 2 t 2 ) ( 1 + k 2 t 2 ) , inverse-Jacobi-elliptic-sd 𝑥 𝑘 superscript subscript 0 𝑥 𝑡 1 superscript superscript 𝑘 2 superscript 𝑡 2 1 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle\operatorname{arcsd}\left(x,k\right)=\int_{0}^{x}% \frac{\mathrm{d}t}{\sqrt{(1-{k^{\prime}}^{2}t^{2})(1+k^{2}t^{2})}},}}
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    - 1 / k x 1 / k 1 superscript 𝑘 𝑥 1 superscript 𝑘 {\displaystyle{\displaystyle-1/k^{\prime}\leq x\leq 1/k^{\prime}}}
    0 references