DLMF:22.19.E2 (Q7176)

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DLMF:22.19.E2
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    Statements

    Defining formula
    sin ⁡ ( 1 2 ⁢ θ ⁢ ( t ) ) = sin ⁡ ( 1 2 ⁢ α ) ⁢ sn ⁡ ( t + K , sin ⁡ ( 1 2 ⁢ α ) ) , 1 2 𝜃 𝑡 1 2 𝛼 Jacobi-elliptic-sn 𝑡 𝐾 1 2 𝛼 {\displaystyle{\displaystyle\sin\left(\tfrac{1}{2}\theta(t)\right)=\sin\left(% \frac{1}{2}\alpha\right)\operatorname{sn}\left(t+K,\sin\left(\tfrac{1}{2}% \alpha\right)\right),}}
    0 references
    DLMF id
    DLMF:22.19.E2
    0 references
    Symbols used
    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.m2adec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1adec
    0 references
     
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