I have data points — denoted by `Fk`— covering quite a large range $(1,\,10^{1010})$. I plotted them with `ListLogPlot`. Then I tried to fit the data points using `NonlinearModelFit`, and now I have two problems:

1. Fitting the data points

        fit = NonlinearModelFit[Fk[300], a*k^(B*k), {a, B}, k] 

   gives `1 k^1` for the fitted model.

    However, fitting the data points with: 

        fit2 = NonlinearModelFit[Fk[300], a*k^(b*c*k), {a, b, c}, k] 

    gives the fitted model `140.714 k^1.16997 k` which I completely do not unterstand. I mean why should the output change upon inserting the variable $c$, which could also be combined with $b$ such that say $b\,c= B$ and `fit` should be equal to `fit2`.

2. If I now plot the data $F_k$ vs. $k$ together with the fitted model, the fitted curve ends at some value of $k \approx 120$, and I do not unterstand why. My code for this is

        Show[{ListLogPlot[Fk[300], PlotStyle -> Red], LogPlot[fit2[k], {k, 0, 300}]}]

[![plot][1]][1]

Red dots = data points; blue line = fitted curve

  [1]: https://i.sstatic.net/I9Oex.jpg