# 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.

Anybody?

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

Dale
Mentor
2021 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.