DLMF:22.14.E6 (Q7081): Difference between revisions

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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.m1adec

Latest revision as of 15:23, 2 January 2020

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DLMF:22.14.E6
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    Statements

    Defining formula
    ∫ nd ⁡ ( x , k ) ⁢ d x = k ′ - 1 ⁢ Arccos ⁡ ( cd ⁡ ( x , k ) ) . Jacobi-elliptic-nd 𝑥 𝑘 𝑥 superscript superscript 𝑘 ′ 1 multivalued-inverse-cosine Jacobi-elliptic-cd 𝑥 𝑘 {\displaystyle{\displaystyle\int\operatorname{nd}\left(x,k\right)\mathrm{d}x={% k^{\prime}}^{-1}\operatorname{Arccos}\left(\operatorname{cd}\left(x,k\right)% \right).}}
    0 references
    DLMF id
    DLMF:22.14.E6
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m2abdec
    0 references
    Jacobian elliptic function
    Defining formula
    nd ⁡ ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m3aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    general arccosine function
    Defining formula
    Arccos ⁡ z multivalued-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccos}\NVar{z}}}
    xml-id
    C4.S23.E2.m2aadec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1edec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1edec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1adec
    0 references
     
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