DLMF:13.20.E15 (Q4604): Difference between revisions

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

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DLMF:13.20.E15
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    Statements

    - ζ ζ 2 - α 2 - α 2 arccosh ( - ζ α ) = - X μ + 2 κ μ ln ( 2 κ - X - x 2 κ 2 - μ 2 ) + 2 ln ( μ X + 2 μ 2 - κ x 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 2 𝜅 𝑋 𝑥 2 superscript 𝜅 2 superscript 𝜇 2 2 𝜇 𝑋 2 superscript 𝜇 2 𝜅 𝑥 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{2\kappa-X-x}{2\sqrt{\kappa^{2}-\mu^{2}}}\right)+2% \ln\left(\frac{\mu X+2\mu^{2}-\kappa x}{x\sqrt{\kappa^{2}-\mu^{2}}}\right),}}
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    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