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DLMF:22.15.E8 - MaRDI portal

DLMF:22.15.E8 (Q7796)

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DLMF:22.15.E8
No description defined

    Statements

    DLMF defining formula
    ξ = ( - 1 ) m ⁢ arcsn ⁡ ( x , k ) + 2 ⁢ m ⁢ K , 𝜉 superscript 1 𝑚 inverse-Jacobi-elliptic-sn 𝑥 𝑘 2 𝑚 𝐾 {\displaystyle{\displaystyle\xi=(-1)^{m}\operatorname{arcsn}\left(x,k\right)+2% mK,}}
    0 references
    Symbols used
    Legendre’s complete elliptic integral of the first kind
    DLMF defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1acdec
    0 references
    Q12010
    DLMF defining formula
    arcsn ⁡ ( x , k ) inverse-Jacobi-elliptic-sn 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcsn}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m1abdec
    0 references
    real
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1gdec
    0 references
    modulus
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1gdec
    0 references
    solution
    DLMF defining formula
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C22.S15.XMD1.m1bdec
    0 references
    integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C22.S15.XMD4.m1dec
    0 references

    Identifiers

     
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