Let's say I have some data, as a function of a variable [itex]x[/itex]. I want to fit this to the real part of the function(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{A}{1-ix}\left(1+\sum_{n=1}^\infty\frac{c_n}{(1-ix)^n}\right)[/tex]

by numerically fitting the first [itex]N[/itex] of the [itex]c_n[/itex]'s ([itex]A[/itex] is fixed). I tried something like

However, this way does not work. For the case [itex]N=5[/itex], I put in the summation explicitly, calling my parameters c1, c2, etc, and it produces different (better) results than the above code. This is not feasible if I want the first 100 or 1000 coefficients, so any help with the above method would be appreciated. Thanks in advance.Code (Text):

A = 1; N = 100;

fit = FindFit[data, Re[A(1+Sum[c[k]/(1-i x)^k,{k,1,N}])], Table[c[k], {k,1,N}], x];

Plot[Re[A(1+Sum[c[k]/(1-i x)^k,{k,1,N}])]/.fit, {x,0,10}]

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# Mathematica, fitting an arbitrary number of parameters

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