How Can I Find the Inverse Laplace Transform of These Functions?

[drdolittle]

Can somebody help me to find the inverse laplace transform of these functions

exp(sqrt(1+s))
sqrt(1+s))

I tried solving these using MATLAB and mathematica,it is unable to give a result.
Do they contain any closed form solution or should i have to go for a numerical technique to solve them?If so,anybody aware of accurate and efficient numerical technique?
Currently iam using a Numerical technique using Haar wavelet matrices but doubt on its validity in terms of both accuracy and efficiency.
sombeody please help me.Thanx in advance

regards
drdolittle

 

[rayveldkamp]

Try replacing sqrt(1+s) by it Taylor series, 1+x/2 -(x^2)/8 +(x^3)/16 +...
then express the inverse Laplace transform as an infinite sum.

Ray

 

[Tide]

That's a tough one! Would an asymptotic expansion be of any use?

 

[drdolittle]

thanx for the suggestion.
but if we use a taylor series we have to truncate at some point of time and i presume it will not be more efficient than numerical techniques...i hope so

Regards
drdolittle