DLMF:22.15.E21 (Q7116): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m3ajdec
Property / Symbols used
 
Property / Symbols used: Q12017 / rank
 
Normal rank
Property / Symbols used: Q12017 / qualifier
 
Defining formula:

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

\aJacobiellnsk@{\NVar{x}}{\NVar{k}}
Property / Symbols used: Q12017 / qualifier
 
xml-id: C22.S15.SS1.p1.m7adec
Property / Symbols used
 
Property / Symbols used: Q12003 / rank
 
Normal rank
Property / Symbols used: Q12003 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12003 / qualifier
 
xml-id: C22.S1.XMD1.m1tdec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1tdec

Latest revision as of 15:30, 2 January 2020

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DLMF:22.15.E21
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    Statements

    arcns ( x , k ) = x d t ( t 2 - 1 ) ( t 2 - k 2 ) , inverse-Jacobi-elliptic-ns 𝑥 𝑘 superscript subscript 𝑥 𝑡 superscript 𝑡 2 1 superscript 𝑡 2 superscript 𝑘 2 {\displaystyle{\displaystyle\operatorname{arcns}\left(x,k\right)=\int_{x}^{% \infty}\frac{\mathrm{d}t}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}},}}
    0 references
    DLMF:22.15.E21
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    1 x < 1 𝑥 {\displaystyle{\displaystyle 1\leq x<\infty}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1ajdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3ajdec
    0 references
    arcns ( x , k ) inverse-Jacobi-elliptic-ns 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcns}\left(\NVar{x},\NVar{k}\right)}}
    C22.S15.SS1.p1.m7adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C22.S1.XMD1.m1tdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1tdec
    0 references