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December 9th, 2017, 08:56 AM   #1
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Inequality

Let $\nu>1$ be a parameter.

For all $t>0,\;\;\;$ we consider




$A(t)=\frac{1-cos(t\sqrt{4\nu-1})}{4\nu-1}-(\cosh(t)-1)$

$g(t)=\frac{2A(t)}{\frac{sin(t\sqrt{4\nu-1})}{\sqrt{4\nu-1}}+\sinh(t)+A(t)}$

$f(t)=\frac{\sqrt{\nu }\;t^{\frac{3}{2}}\;e^{-t\nu^\frac{1}{3}}}{ln(1-g(t))}$

>I want to prove that there exists a constant $c>0$ which dosn't depend on the parameter $\nu$ such that:

$$f(t)\le c$$ for all $t>0$

Please help me to do so.

Thanks.

Last edited by mona123; December 9th, 2017 at 09:33 AM.
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