DLMF:22.16.E21 (Q7141): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12003 / rank
 
Normal rank
Property / Symbols used: Q12003 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12003 / qualifier
 
xml-id: C22.S1.XMD1.m1tdec

Revision as of 15:34, 2 January 2020

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DLMF:22.16.E21
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    Statements

    Defining formula
    ℰ ⁡ ( x , k ) = - ∫ 0 x dc 2 ⁡ ( t , k ) ⁢ d t + x + sn ⁡ ( x , k ) ⁢ dc ⁡ ( x , k ) , Jacobi-Epsilon 𝑥 𝑘 superscript subscript 0 𝑥 Jacobi-elliptic-dc 2 𝑡 𝑘 𝑡 𝑥 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-dc 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=-\int_{0}^{x}{% \operatorname{dc}^{2}}\left(t,k\right)\mathrm{d}t+x+\operatorname{sn}\left(x,k% \right)\operatorname{dc}\left(x,k\right),}}
    0 references
    DLMF id
    DLMF:22.16.E21
    0 references
    Symbols used
    Jacobi’s epsilon function
    Defining formula
    ℰ ⁡ ( x , k ) Jacobi-Epsilon 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S16.E14.m2agdec
    0 references
    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
    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.m2agdec
    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
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1tdec
    0 references
     
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