DLMF:22.15.E12 (Q7107): 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.m3aadec

Revision as of 15:28, 2 January 2020

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DLMF:22.15.E12
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    Statements

    Defining formula
    arcsn ⁡ ( x , k ) = ∫ 0 x d t ( 1 - t 2 ) ⁢ ( 1 - k 2 ⁢ t 2 ) , inverse-Jacobi-elliptic-sn 𝑥 𝑘 superscript subscript 0 𝑥 𝑡 1 superscript 𝑡 2 1 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle\operatorname{arcsn}\left(x,k\right)=\int_{0}^{x}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E12
    0 references
    constraint
    - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
     
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