DLMF:22.14.E13 (Q7088)

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DLMF:22.14.E13
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    Statements

    Defining formula
    ∫ d x sn ⁡ ( x , k ) = ln ⁡ ( sn ⁡ ( x , k ) cn ⁡ ( x , k ) + dn ⁡ ( x , k ) ) , 𝑥 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-cn 𝑥 𝑘 Jacobi-elliptic-dn 𝑥 𝑘 {\displaystyle{\displaystyle\int\frac{\mathrm{d}x}{\operatorname{sn}\left(x,k% \right)}=\ln\left(\frac{\operatorname{sn}\left(x,k\right)}{\operatorname{cn}% \left(x,k\right)+\operatorname{dn}\left(x,k\right)}\right),}}
    0 references
    DLMF id
    DLMF:22.14.E13
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2abdec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2acdec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2abdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ahdec
    0 references
     
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