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

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    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
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