# Math Help - Inverse Laplace transform for small 's', Taylor expansion

1. ## Inverse Laplace transform for small 's', Taylor expansion

Dear all,

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!

Best regards, perr