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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11988 / rank
 
Normal rank
Property / Symbols used: Q11988 / qualifier
 
Defining formula:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11988 / qualifier
 
xml-id: C22.S1.XMD5.m1cdec

Latest revision as of 15:29, 2 January 2020

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DLMF:22.15.E16
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    Statements

    Defining formula
    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})}},}}
    0 references
    DLMF id
    DLMF:22.15.E16
    0 references
    constraint
    - 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
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    Q12012
    Defining formula
    arcsd ⁡ ( x , k ) inverse-Jacobi-elliptic-sd 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcsd}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m4adec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1odec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1odec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1cdec
    0 references
     
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