Inverse Laplace transform for small 's', Taylor expansion

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SUMMARY

The discussion focuses on the inverse Laplace transform of the function F(s) = 1 / (s - K(s)), where K(s) is defined as K(s) = -1/2 + i/(2*Pi) * ln[(Lambda - (b+i*s))/(b + i*s)]. The parameters Lambda and b are specified as Lambda=1000 and b=10. The user seeks to explore the inverse Laplace transform of F(s) as s approaches zero, suggesting a Taylor expansion approach to express F(s) in the form A/s + B + C*s + D*s^2 + ... for further analysis. References to Wikipedia articles on Laplace transforms are provided for additional context.

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perr
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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
 

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