DLMF:22.16.E19 (Q7139): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1afdec

Revision as of 15:33, 2 January 2020

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DLMF:22.16.E19
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    Statements

    Defining formula
    ℰ ⁡ ( x , k ) = k 2 ⁢ k ′ 2 ⁢ ∫ 0 x sd 2 ⁡ ( t , k ) ⁢ d t + k ′ 2 ⁢ x + k 2 ⁢ sn ⁡ ( x , k ) ⁢ cd ⁡ ( x , k ) , Jacobi-Epsilon 𝑥 𝑘 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 superscript subscript 0 𝑥 Jacobi-elliptic-sd 2 𝑡 𝑘 𝑡 superscript superscript 𝑘 ′ 2 𝑥 superscript 𝑘 2 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-cd 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=k^{2}{k^{\prime}}^{2}% \int_{0}^{x}{\operatorname{sd}^{2}}\left(t,k\right)\mathrm{d}t+{k^{\prime}}^{2% }x+k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd}\left(x,k\right),}}
    0 references
    DLMF id
    DLMF:22.16.E19
    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.m2aedec
    0 references
    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.m2aadec
    0 references
    Jacobian elliptic function
    Defining formula
    sd ⁡ ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m2adec
    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.m2aedec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
     
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