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!

Best regards, perr

Attachments

• 80.8 KB Views: 81

fresh_42

Mentor
2018 Award
Have a look on
and especially the links in the second one.

"Inverse Laplace transform for small 's', Taylor expansion"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving