DLMF:13.21.E11 (Q4619): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec

Revision as of 15:18, 2 January 2020

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DLMF:13.21.E11
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    Statements

    test
    4 ⁢ μ 2 - κ ⁢ ζ - μ ⁢ ln ⁡ ( 2 ⁢ μ + 4 ⁢ μ 2 - κ ⁢ ζ 2 ⁢ μ - 4 ⁢ μ 2 - κ ⁢ ζ ) = 1 2 ⁢ X + μ ⁢ ln ⁡ ( x ⁢ κ 2 - μ 2 2 ⁢ μ 2 - κ ⁢ x + μ ⁢ X ) + κ ⁢ ln ⁡ ( 2 ⁢ κ 2 - μ 2 2 ⁢ κ - x - X ) , 4 superscript 𝜇 2 𝜅 𝜁 𝜇 2 𝜇 4 superscript 𝜇 2 𝜅 𝜁 2 𝜇 4 superscript 𝜇 2 𝜅 𝜁 1 2 𝑋 𝜇 𝑥 superscript 𝜅 2 superscript 𝜇 2 2 superscript 𝜇 2 𝜅 𝑥 𝜇 𝑋 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 2 𝜅 𝑥 𝑋 {\displaystyle{\displaystyle\sqrt{4\mu^{2}-\kappa\zeta}-\mu\ln\left(\frac{2\mu% +\sqrt{4\mu^{2}-\kappa\zeta}}{2\mu-\sqrt{4\mu^{2}-\kappa\zeta}}\right)=\tfrac{% 1}{2}X+\mu\ln\left(\frac{x\sqrt{\kappa^{2}-\mu^{2}}}{2\mu^{2}-\kappa x+\mu X}% \right)+\kappa\ln\left(\frac{2\sqrt{\kappa^{2}-\mu^{2}}}{2\kappa-x-X}\right),}}
    0 references
    DLMF id
    DLMF:13.21.E11
    0 references
    constraint
    0 < x ≤ 2 ⁢ κ - 2 ⁢ κ 2 - μ 2 0 𝑥 2 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 {\displaystyle{\displaystyle 0<x\leq 2\kappa-2\sqrt{\kappa^{2}-\mu^{2}}}}
    0 references
    Symbols used
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
     
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