DLMF:22.14.E9 (Q7084): 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.m1cdec

Latest revision as of 15:24, 2 January 2020

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DLMF:22.14.E9
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    Statements

    Defining formula
    ∫ sc ⁡ ( x , k ) ⁢ d x = k ′ - 1 ⁢ ln ⁡ ( dc ⁡ ( x , k ) + k ′ ⁢ nc ⁡ ( x , k ) ) . Jacobi-elliptic-sc 𝑥 𝑘 𝑥 superscript superscript 𝑘 ′ 1 Jacobi-elliptic-dc 𝑥 𝑘 superscript 𝑘 ′ Jacobi-elliptic-nc 𝑥 𝑘 {\displaystyle{\displaystyle\int\operatorname{sc}\left(x,k\right)\mathrm{d}x={% k^{\prime}}^{-1}\ln\left(\operatorname{dc}\left(x,k\right)+k^{\prime}% \operatorname{nc}\left(x,k\right)\right).}}
    0 references
    DLMF id
    DLMF:22.14.E9
    0 references
    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.m3abdec
    0 references
    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.m3abdec
    0 references
    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.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1hdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1hdec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1cdec
    0 references
     
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