Inverse Laplace transform for small 's', Taylor expansion

[perr]

Dear all,

This question is close to the post "Laplace transform of a Taylor series expansion" in PhysicsForums.com, dated Jul06-09. This is my problem:

Consider the Laplace transform


F(s) = 1 / ( s - K(s) ) ,

where

K(s) = -1/2 + i/(2*Pi) * ln[ ( Lambda - (b+i*s) )/( b + i*s ) ].


See PDF-attachment. ( 'Lambda' and 'b' are real numbers, typically 'Lambda=1000' and 'b=10'). I want to explore the inverse Laplace transform of this F(s) for large time (t-> infinity), i.e. s->0.

How can this be done?

Perhaps write/expand F(s) on the form F(s) = A/s + B + C*s + D*s^2 + ... , and then take inverse Laplace transform of each these terms?

I appreciate any help!

perr

 

[fresh_42]

Have a look on
https://en.wikipedia.org/wiki/Laplace_transformhttps://en.wikipedia.org/wiki/Inverse_Laplace_transformand especially the links in the second one.