Can Mathematica Handle Complex Inverse Laplace Transforms with Bessel Functions?

[EngWiPy]

Hello,

I have the following Laplace function:

$$\frac{\left[2\sqrt{a\,s}K_1\left(2\sqrt{a\,s}\right)\right]^N}{s}$$

where N and a are constants and K1 is the modified Bessel function of the second kind and order 1. I need to find the inverse Laplace transform at a specific value. Can I do that in Mathematica?

Thanks

 

[Bill Simpson]

I do not believe so.

It seems that it cannot even do this simpler problem

http://www.wolframalpha.com/input/?i=InverseLaplaceTransform[BesselY[1,Sqrt[s]]/Sqrt[s],s,t]

It can't even do this

http://www.wolframalpha.com/input/?i=InverseLaplaceTransform[BesselY[1,s]/s,s,t]

Check this carefully before depending on it

If I have not made a mistake and
if Mathematica cannot do this and
if you can convincingly demonstrate that there is a solution that is valid over a significant domain
then we can try to coax them to incorporating that into a future release,
but I would urge you to not hold your breath waiting for this.

Is there any chance that you can find an acceptable approximation to your function which does have an Inverse Laplace?

 

[EngWiPy]

I do not believe so.

It seems that it cannot even do this simpler problem

http://www.wolframalpha.com/input/?i=InverseLaplaceTransform[BesselY[1,Sqrt[s]]/Sqrt[s],s,t]

It can't even do this

http://www.wolframalpha.com/input/?i=InverseLaplaceTransform[BesselY[1,s]/s,s,t]

Check this carefully before depending on it

If I have not made a mistake and
if Mathematica cannot do this and
if you can convincingly demonstrate that there is a solution that is valid over a significant domain
then we can try to coax them to incorporating that into a future release,
but I would urge you to not hold your breath waiting for this.

Is there any chance that you can find an acceptable approximation to your function which does have an Inverse Laplace?

This is the problem, there is no closed form expression known for this. I thought Mathematica would do the numerical inverse Laplace transform. I think I need to do that manually now. Thanks