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Re: InverseLaplaceTransform
*To*: mathgroup at smc.vnet.net
*Subject*: [mg26681] Re: InverseLaplaceTransform
*From*: Roland Franzius <Roland.Franzius at uos.de>
*Date*: Wed, 17 Jan 2001 00:47:30 -0500 (EST)
*Organization*: Universitaet Osnabrueck
*References*: <93ramm$57u@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Knut Henning Schroder wrote:
>
> I try to find a symbolic solution of:
> InverseLaplaceTransform[(s + a)/(b s Sqrt[s] + c Sqrt[s] + d), s, t]
> for electrode processes in electrochemistry. Can you help me?
> Thank you and regards,
> Knut Schroder
You may perform a partial fraction decomposition of the denominator in
the variable x=Sqrt[s]. Then, you get a linear combination of
functions s/(Sqrt[s]-A), a * 1/(Sqrt[s]-A) and something similar for
the other zeros B,C of b x^3 + c x + d ==0.
The inverse LaplaceTransform of the simple terms are
InvLap[1/(Sqrt[s]-A),s,t] = f[t] = 1/Sqrt[Pi t] A e^(A^2 t) Erfc[A
Sqrt[t]]
InvLap[s/(Sqrt[s]-A),s,t] = -d/dt f[t]
Hope it helps
regards
--
Roland Franzius
+++ exactly <<n>> lines of this message have value <<FALSE>> +++
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