Integral of exp(-a*m)*sech^{1/m}(a*m) dm

Hi,

I would like at least some hints to compute the following integral :

$\displaystyle \int_0^\infty exp(-ax) \text{cosh}^{-1/x}(ax) dx $

As a known result we have :
$\displaystyle \lim_{x->0} \text{cosh}^{-1/x}(ax) = 1$

So the function should behave well and be integrable but mathematica gives no anwser for it...

Can somebody help ?

Thanks

Alexis

Quote:

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Originally Posted by AlexisM

Hi,

I would like at least some hints to compute the following integral :

$\displaystyle \int_0^\infty exp(-a*x) \text{cosh}^{-1/x}(a*x) dx $

As a known result we have :
$\displaystyle \lim_{x->0} \text{cosh}^{-1/x}(a*x) = 1$

So the function should behave well and be integrable but mathematica gives no anwser for it...

Can somebody help ?

Thanks

Alexis

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Can you provide some background, why you need this integral (the problem it is part of ...) what if any level/ quality of approximation would be acceptable for the integral, ...

CB