DLMF:22.15.E23 (Q7118): Difference between revisions

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‎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.m1hdec

Latest revision as of 15:30, 2 January 2020

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DLMF:22.15.E23
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    Statements

    Defining formula
    arccs ⁡ ( x , k ) = ∫ x ∞ d t ( 1 + t 2 ) ⁢ ( t 2 + k ′ 2 ) , inverse-Jacobi-elliptic-cs 𝑥 𝑘 superscript subscript 𝑥 𝑡 1 superscript 𝑡 2 superscript 𝑡 2 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle\operatorname{arccs}\left(x,k\right)=\int_{x}^{% \infty}\frac{\mathrm{d}t}{\sqrt{(1+t^{2})(t^{2}+{k^{\prime}}^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E23
    0 references
    constraint
    - ∞ < x < ∞ 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
    0 references
    Q12019
    Defining formula
    arccs ⁡ ( x , k ) inverse-Jacobi-elliptic-cs 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arccs}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m12adec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1vdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1vdec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1hdec
    0 references
     
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