DLMF:22.15.E13 (Q7108): Difference between revisions

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Property / constraint
 

- 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}

-1\leq x\leq 1
Property / constraint: - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: Q12008 / rank
 
Normal rank
Property / Symbols used: Q12008 / qualifier
 
test:

arccn ⁡ ( x , k ) inverse-Jacobi-elliptic-cn 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arccn}\left(\NVar{x},\NVar{k}\right)}}

\aJacobiellcnk@{\NVar{x}}{\NVar{k}}
Property / Symbols used: Q12008 / qualifier
 
xml-id: C22.S15.SS1.p1.m2acdec
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.m1ldec
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.m1ldec

Latest revision as of 14:28, 2 January 2020

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DLMF:22.15.E13
No description defined

    Statements

    test
    arccn ⁡ ( x , k ) = ∫ x 1 d t ( 1 - t 2 ) ⁢ ( k ′ 2 + k 2 ⁢ t 2 ) , inverse-Jacobi-elliptic-cn 𝑥 𝑘 superscript subscript 𝑥 1 𝑡 1 superscript 𝑡 2 superscript superscript 𝑘 ′ 2 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle\operatorname{arccn}\left(x,k\right)=\int_{x}^{1}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})({k^{\prime}}^{2}+k^{2}t^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E13
    0 references
    constraint
    - 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q12008
    test
    arccn ⁡ ( x , k ) inverse-Jacobi-elliptic-cn 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arccn}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m2acdec
    0 references
    Q12003
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1ldec
    0 references
    Q11984
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1ldec
    0 references
     
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