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

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Property / Symbols used
 
Property / Symbols used: Q12019 / rank
 
Normal rank
Property / Symbols used: Q12019 / qualifier
 
test:

arccs ( x , k ) inverse-Jacobi-elliptic-cs 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arccs}\left(\NVar{x},\NVar{k}\right)}}

\aJacobiellcsk@{\NVar{x}}{\NVar{k}}
Property / Symbols used: Q12019 / qualifier
 
xml-id: C22.S15.SS1.p1.m12adec
Property / Symbols used
 
Property / Symbols used: Q12003 / rank
 
Normal rank
Property / Symbols used: Q12003 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12003 / qualifier
 
xml-id: C22.S1.XMD1.m1vdec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1vdec
Property / Symbols used
 
Property / Symbols used: Q11988 / rank
 
Normal rank
Property / Symbols used: Q11988 / qualifier
 
test:

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

k^{\prime}
Property / Symbols used: Q11988 / qualifier
 
xml-id: C22.S1.XMD5.m1hdec

Latest revision as of 14:30, 2 January 2020

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DLMF:22.15.E23
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    Statements

    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
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    - < x < 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aldec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aldec
    0 references
    arccs ( x , k ) inverse-Jacobi-elliptic-cs 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arccs}\left(\NVar{x},\NVar{k}\right)}}
    C22.S15.SS1.p1.m12adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C22.S1.XMD1.m1vdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1vdec
    0 references
    k superscript 𝑘 {\displaystyle{\displaystyle k^{\prime}}}
    C22.S1.XMD5.m1hdec
    0 references