## Tricks for inverting a Laplace Transform, part III

*This is a continuation of the series of articles on Laplace transforms… You can also have a look at part I (guesses based on series expansions), part II (products and convolutions), part IV (substitutions), and part V (pole decomposition).*

This time we will cover the following inverse Laplace problems:

The basic result that can be used for such problems is the Laplace transform of the Bessel function:

Now, using

,

and by rescaling , one finds that is solved by:

Have fun!

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[…] After a few less technical posts recently, I now continue the series of articles on tricks for the inversion of Laplace transforms. You can find the previous parts here: part I, part II, part III. […]

Tricks for inverting a Laplace Transform, part IV: Substitutions « inordinatumNovember 4, 2012 at 2:14 pm

[…] series of posts on Laplace Transform inversion. You can find the subsequent articles here: part II, part III, part IV. […]

Tricks for inverting a Laplace Transform, part I « inordinatumNovember 7, 2012 at 8:29 pm

[…] series of posts on Laplace Transform inversion. You can find the subsequent articles here: part I, part III, part IV. […]

Tricks for inverting a Laplace Transform, part II « inordinatumNovember 9, 2012 at 9:10 pm

[…] parts here: part I (guesses based on series expansions), part II (products and convolutions), part III, part IV […]

Tricks for inverting a Laplace Transform, part V: Pole Decomposition | inordinatumApril 15, 2013 at 10:27 pm

Typo: e^c x –> e^(-cx)

aJuly 6, 2015 at 10:01 am

Thanks! I agree that the bracketing of the exponent was wrong, I’ve now fixed that in the post and also added an extra step. However I think the sign was correct…

inordinatumJuly 7, 2015 at 9:30 pm