       Fitting a inverse function from complicated integral

• To: mathgroup at smc.vnet.net
• Subject: [mg87210] Fitting a inverse function from complicated integral
• From: tibor dubaj <t.dubaj at gmail.com>
• Date: Fri, 4 Apr 2008 02:57:54 -0500 (EST)

```Dear Group,

I need to Fit this experimental data {x, OOT}:

data = {
{1, 444.6},
{3, 455.15},
{5, 464.81},
{7, 467.79},
{10, 469.01},
{15, 480.28}}

But there is a big problem with model equation:

x = Integrate[A*Exp[-B/T], {T, 0, OOT}, Assumptions -> A > 0 && B > 0
&& OOT > 0]

So, after integration:

x = A (Exp[-B/OOT] OOT - B Gamma[0, B/OOT])

I need to obtain a INVERSE function, i.e. OOT = f(x) and then find
(e.g. via FindFit) best fitting parameters A, B.

I have tried Series expansion, PadeApproximant etc., but every
approximation of mentioned
model contain A*Exp[-B/T], so I cannot find inverse function.

Can Somebody help me with this problem?

*****************
\$Version
6.0 for Microsoft Windows (32-bit) (February 7, 2008)

```

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