DLMF:22.15.E5 (Q7100)

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DLMF:22.15.E5
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    Statements

    Defining formula
    - K ≤ arcsn ⁡ ( x , k ) ≤ K , 𝐾 inverse-Jacobi-elliptic-sn 𝑥 𝑘 𝐾 {\displaystyle{\displaystyle-K\leq\operatorname{arcsn}\left(x,k\right)\leq K,}}
    0 references
    DLMF id
    DLMF:22.15.E5
    0 references
    Symbols used
    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
    Q12007
    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.m1aadec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1ddec
    0 references
     
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