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DLMF:22.15.E5 - MaRDI portal

DLMF:22.15.E5 (Q7793)

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DLMF:22.15.E5
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    Statements

    DLMF defining formula
    - K ≀ arcsn ⁑ ( x , k ) ≀ K , 𝐾 inverse-Jacobi-elliptic-sn π‘₯ π‘˜ 𝐾 {\displaystyle{\displaystyle-K\leq\operatorname{arcsn}\left(x,k\right)\leq K,}}
    0 references
    Symbols used
    Legendre’s complete elliptic integral of the first kind
    DLMF defining formula
    K ⁑ ( k ) complete-elliptic-integral-first-kind-K π‘˜ {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1adec
    0 references
    Q12010
    DLMF defining formula
    arcsn ⁑ ( x , k ) inverse-Jacobi-elliptic-sn π‘₯ π‘˜ {\displaystyle{\displaystyle\operatorname{arcsn}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m1aadec
    0 references
    real
    DLMF defining formula
    x π‘₯ {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1ddec
    0 references
    modulus
    DLMF defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1ddec
    0 references

    Identifiers

     
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