怎么够买北加州大学文凭毕业证【仿证 微fuk7778】acoshS

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11: 18.15 Asymptotic Approximations

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$$\zeta ={\left(\frac{3}{4}\left(\sqrt{x^2-x}-\mathrm{arccosh}\left(\sqrt{x}\right)\right)\right)}^{\frac{2}{3}},$$ $x\ge 1$.

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12: 14.15 Uniform Asymptotic Approximations

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14.15.27 $$\frac{1}{2}\zeta {\left({\zeta }^2-{\alpha }^2\right)}^{1/2}-\frac{1}{2}{\alpha }^2\mathrm{arccosh}\left(\frac{\zeta }{\alpha }\right)={\left(1-a^2\right)}^{1/2}\mathrm{arctanh}\left(\frac{1}{x}{\left(\frac{x^2-a^2}{1-a^2}\right)}^{1/2}\right)-\mathrm{arccosh}\left(\frac{x}{a}\right),$$ , ,

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Symbols:

$\mathrm{arccosh}z$: inverse hyperbolic cosine function, $\mathrm{arctanh}z$: inverse hyperbolic tangent function, $x$: real variable, $a$ , $\zeta$ and $\alpha$

Permalink:

http://dlmf.nist.gov/14.15.E27

Encodings:

pMML, png, TeX

See also:

Annotations for §14.15(v), §14.15 and Ch.14

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13: 13.8 Asymptotic Approximations for Large Parameters

… ►where $w=\mathrm{arccosh}\left(1+{(2a)}^{-1}x\right)$, and $\beta =(w+\sinh w)/2$. …