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DLMF:22.6.E3 - MaRDI portal

DLMF:22.6.E3 (Q7630)

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DLMF:22.6.E3
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    Statements

    DLMF defining formula
    k ′ 2 ⁢ sc 2 ⁡ ( z , k ) + 1 = dc 2 ⁡ ( z , k ) = k ′ 2 ⁢ nc 2 ⁡ ( z , k ) + k 2 , superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 2 𝑧 𝑘 1 Jacobi-elliptic-dc 2 𝑧 𝑘 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-nc 2 𝑧 𝑘 superscript 𝑘 2 {\displaystyle{\displaystyle{k^{\prime}}^{2}{\operatorname{sc}^{2}}\left(z,k% \right)+1={\operatorname{dc}^{2}}\left(z,k\right)={k^{\prime}}^{2}{% \operatorname{nc}^{2}}\left(z,k\right)+k^{2},}}
    0 references
    Symbols used
    Jacobian elliptic function
    DLMF 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
    DLMF defining formula
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3adec
    0 references
    Jacobian elliptic function
    DLMF defining formula
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2adec
    0 references
    complex
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1bdec
    0 references
    modulus
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1bdec
    0 references
    complementary modulus
    DLMF defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1dec
    0 references

    Identifiers

     
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