DLMF:22.14.E2 (Q7077): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}

\Jacobielldnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m2aadec
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.m1aadec
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.m3aadec
Property / Symbols used
 
Property / Symbols used: general arccosine function / rank
 
Normal rank
Property / Symbols used: general arccosine function / qualifier
 
test:

Arccos ⁡ z multivalued-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccos}\NVar{z}}}

\Acos@@{\NVar{z}}
Property / Symbols used: general arccosine function / qualifier
 
xml-id: C4.S23.E2.m2adec
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.m1adec
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.m1adec

Latest revision as of 14:22, 2 January 2020

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DLMF:22.14.E2
No description defined

    Statements

    test
    ∫ cn ⁡ ( x , k ) ⁢ d x = k - 1 ⁢ Arccos ⁡ ( dn ⁡ ( x , k ) ) , Jacobi-elliptic-cn 𝑥 𝑘 𝑥 superscript 𝑘 1 multivalued-inverse-cosine Jacobi-elliptic-dn 𝑥 𝑘 {\displaystyle{\displaystyle\int\operatorname{cn}\left(x,k\right)\mathrm{d}x=k% ^{-1}\operatorname{Arccos}\left(\operatorname{dn}\left(x,k\right)\right),}}
    0 references
    DLMF id
    DLMF:22.14.E2
    0 references
    Symbols used
    Jacobian elliptic function
    test
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2aadec
    0 references
    Jacobian elliptic function
    test
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    general arccosine function
    test
    Arccos ⁡ z multivalued-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccos}\NVar{z}}}
    xml-id
    C4.S23.E2.m2adec
    0 references
    Q12003
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1adec
    0 references
    Q11984
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1adec
    0 references
     
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