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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

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