DLMF:13.20.E13 (Q4602): Difference between revisions

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Property / 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}}}}

x\geq 2\kappa+2\sqrt{\kappa^{2}-\mu^{2}}
Property / 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}}}} / rank
 
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Revision as of 16:49, 30 December 2019

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DLMF:13.20.E13
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    Statements

    ζ ζ 2 - α 2 - α 2 arccosh ( ζ α ) = X μ - 2 κ μ ln ( X + x - 2 κ 2 κ 2 - μ 2 ) - 2 ln ( κ x - μ X - 2 μ 2 x κ 2 - μ 2 ) , 𝜁 superscript 𝜁 2 superscript 𝛼 2 superscript 𝛼 2 hyperbolic-inverse-cosine 𝜁 𝛼 𝑋 𝜇 2 𝜅 𝜇 𝑋 𝑥 2 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 2 𝜅 𝑥 𝜇 𝑋 2 superscript 𝜇 2 𝑥 superscript 𝜅 2 superscript 𝜇 2 {\displaystyle{\displaystyle\zeta\sqrt{\zeta^{2}-\alpha^{2}}-\alpha^{2}% \operatorname{arccosh}\left(\frac{\zeta}{\alpha}\right)=\frac{X}{\mu}-\frac{2% \kappa}{\mu}\ln\left(\frac{X+x-2\kappa}{2\sqrt{\kappa^{2}-\mu^{2}}}\right)-2% \ln\left(\frac{\kappa x-\mu X-2\mu^{2}}{x\sqrt{\kappa^{2}-\mu^{2}}}\right),}}
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    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}}}}
    0 references