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I am attempting to fit a function with three free parameters to a set of data points. I get the error: "Power: Infinite expression 1/0 encountered."

The function in question is:

fit = 
  (Exp[-x* (a + b + c)]* 
    (-1 + Exp[(x* c)]* a* b* 
      (Exp[x* (a + b)]* (a - b) + Exp[x* (b + c)]* (b - c) + 
         Exp[x* (a + c)]* (-a + c)))) /
      ((a - b)* (a - c)* (b - c))

I believe this could be fixed by telling Mathematica to assume that a, b, and c are positive and a != b != c. However it seems that you can't give assumptions to FindFit. Any ideas on how to fix this or work around it?

Context: 

data = 
  {{2, 1.00309*10^-6}, {7, 0.004429942}, {20, 
   1.10643*10^-10}, {40, 0.003376122}, {60, 0.012847188}, {85, 
   0.053338127}, {300, 0.226328628}}

FindFit[data, fit, {a, b, c}, x]

Amended to 

FindFit[data, fit, {{a, .1}, {b, .11}, {c, .12}}, x]

which fixed the issue.

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    $\begingroup$ Please provide a minimal working example needed to reproduce your problem. p.s. e is not E. $\endgroup$
    – Kuba
    Commented Jul 24, 2017 at 20:06
  • 1
    $\begingroup$ Try giving FindFit unequal initial values of {a,b,c} by specifying the parameters as '{{a,1}, {b,2}, {c,3}}`. Some sets of unequal constants may work better than others. $\endgroup$
    – LouisB
    Commented Jul 24, 2017 at 20:47
  • $\begingroup$ Please change the title to something that resembles the question (or justify the relationship of the title to what is given in the text). $\endgroup$
    – JimB
    Commented Jul 25, 2017 at 0:42
  • $\begingroup$ The online documentation does state that FindFit can use constraints: FindFit[data,{expr,cons},pars,vars]. However, one can't use != in the constraints. Your best bet is to use the suggestion by @LouisB. $\endgroup$
    – JimB
    Commented Jul 25, 2017 at 2:46
  • 1
    $\begingroup$ Better that FindFit throw an exception than FindException throw a fit... $\endgroup$
    – Daniel Lichtblau
    Commented Jul 26, 2017 at 16:08

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