DLMF:22.16.E28 (Q7148)

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DLMF:22.16.E28
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    Statements

    Defining formula
    ℰ ⁡ ( x + K , k ) = ℰ ⁡ ( x , k ) + E ⁡ ( k ) - k 2 ⁢ sn ⁡ ( x , k ) ⁢ cd ⁡ ( x , k ) , Jacobi-Epsilon 𝑥 𝐾 𝑘 Jacobi-Epsilon 𝑥 𝑘 complete-elliptic-integral-second-kind-E 𝑘 superscript 𝑘 2 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-cd 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(x+K,k\right)=\mathcal{E}\left(x,k% \right)+E\left(k\right)-k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd% }\left(x,k\right),}}
    0 references
    DLMF id
    DLMF:22.16.E28
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    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.m2andec
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