DLMF:13.21.E21 (Q4629)

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DLMF:13.21.E21
No description defined

    Statements

    Defining formula
    ζ ^ = ( 3 2 ⁢ κ ⁢ ( 1 2 ⁢ X + μ ⁢ ln ⁡ ( x ⁢ κ 2 - μ 2 κ ⁢ x - 2 ⁢ μ 2 - μ ⁢ X ) + κ ⁢ ln ⁡ ( 2 ⁢ κ 2 - μ 2 x - 2 ⁢ κ + X ) ) ) 2 / 3 , ^ 𝜁 superscript 3 2 𝜅 1 2 𝑋 𝜇 𝑥 superscript 𝜅 2 superscript 𝜇 2 𝜅 𝑥 2 superscript 𝜇 2 𝜇 𝑋 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 𝑥 2 𝜅 𝑋 2 3 {\displaystyle{\displaystyle\widehat{\zeta}=\left(\frac{3}{2\kappa}\left(\frac% {1}{2}X+\mu\ln\left(\frac{x\sqrt{\kappa^{2}-\mu^{2}}}{\kappa x-2\mu^{2}-\mu X}% \right)+\kappa\ln\left(\frac{2\sqrt{\kappa^{2}-\mu^{2}}}{x-2\kappa+X}\right)% \right)\right)^{2/3},}}
    0 references
    DLMF id
    DLMF:13.21.E21
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    constraint
    x ≥ 2 ⁢ κ + 2 ⁢ κ 2 - μ 2 𝑥 2 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 {\displaystyle{\displaystyle x\geq 2\kappa+2\sqrt{\kappa^{2}-\mu^{2}}}}
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    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
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    Q11566
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1rdec
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    DLMF:13.21.E18
    Defining formula
    X 𝑋 {\displaystyle{\displaystyle X}}
    xml-id
    C13.S21.XMD5.m1bdec
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