# Mathematica, fitting an arbitrary number of parameters

• Mathematica
Let's say I have some data, as a function of a variable $x$. I want to fit this to the real part of the function

$$\frac{A}{1-ix}\left(1+\sum_{n=1}^\infty\frac{c_n}{(1-ix)^n}\right)$$

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

Code:
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}]
However, this way does not work. For the case $N=5$, 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.

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Anybody?

Redbelly98
Staff Emeritus
Homework Helper
It looks like your code is missing the factor 1 / (1-ix)

Dale
Mentor
2020 Award
Also, in Mathematica the symbol N is protected, use n instead.

It looks like your code is missing the factor 1 / (1-ix)
Yes, it is, but the original code wasn't. That was just me missing it when typing it into here.
Also, in Mathematica the symbol N is protected, use n instead.
That could be the problem, I'll check it later. Thanks for the replies.