DLMF:22.14.E7 (Q7082)

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DLMF:22.14.E7
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    Statements

    Defining formula
    ∫ dc ⁡ ( x , k ) ⁢ d x = ln ⁡ ( nc ⁡ ( x , k ) + sc ⁡ ( x , k ) ) , Jacobi-elliptic-dc 𝑥 𝑘 𝑥 Jacobi-elliptic-nc 𝑥 𝑘 Jacobi-elliptic-sc 𝑥 𝑘 {\displaystyle{\displaystyle\int\operatorname{dc}\left(x,k\right)\mathrm{d}x=% \ln\left(\operatorname{nc}\left(x,k\right)+\operatorname{sc}\left(x,k\right)% \right),}}
    0 references
    DLMF id
    DLMF:22.14.E7
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    Symbols used
    Jacobian elliptic function
    Defining formula
    dc ⁡ ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m3adec
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    Jacobian elliptic function
    Defining formula
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3adec
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    Jacobian elliptic function
    Defining formula
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1fdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1fdec
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