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DLMF:22.15.E9 - MaRDI portal

DLMF:22.15.E9 (Q7797)

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DLMF:22.15.E9
No description defined

    Statements

    DLMF defining formula
    η = ± arccn ⁡ ( x , k ) + 4 ⁢ m ⁢ K , 𝜂 plus-or-minus inverse-Jacobi-elliptic-cn 𝑥 𝑘 4 𝑚 𝐾 {\displaystyle{\displaystyle\eta=\pm\operatorname{arccn}\left(x,k\right)+4mK,}}
    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.m1addec
    0 references
    Q12011
    DLMF defining formula
    arccn ⁡ ( x , k ) inverse-Jacobi-elliptic-cn 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arccn}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m2abdec
    0 references
    real
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1hdec
    0 references
    modulus
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1hdec
    0 references
    solution
    DLMF defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C22.S15.XMD2.m1bdec
    0 references
    integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C22.S15.XMD4.m1adec
    0 references

    Identifiers

     
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