DLMF:22.7.E2 (Q6958)

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DLMF:22.7.E2
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    Statements

    Defining formula
    sn ⁡ ( z , k ) = ( 1 + k 1 ) ⁢ sn ⁡ ( z / ( 1 + k 1 ) , k 1 ) 1 + k 1 ⁢ sn 2 ⁡ ( z / ( 1 + k 1 ) , k 1 ) , Jacobi-elliptic-sn 𝑧 𝑘 1 subscript 𝑘 1 Jacobi-elliptic-sn 𝑧 1 subscript 𝑘 1 subscript 𝑘 1 1 subscript 𝑘 1 Jacobi-elliptic-sn 2 𝑧 1 subscript 𝑘 1 subscript 𝑘 1 {\displaystyle{\displaystyle\operatorname{sn}\left(z,k\right)=\frac{(1+k_{1})% \operatorname{sn}\left(z/(1+k_{1}),k_{1}\right)}{1+k_{1}{\operatorname{sn}^{2}% }\left(z/(1+k_{1}),k_{1}\right)},}}
    0 references
    DLMF id
    DLMF:22.7.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
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1dec
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    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1dec
    0 references
     
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