# How to curve fit an equation with sigma function

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Gaurav Nanajkar on 25 Jul 2019
Edited: Matt J on 29 Jul 2019
Dear all,
I would like to get coefficient C0, C1....CN from the below equation, I have enclosed herewith an excel having x and y co-ordinates.
Can anybody please let me know how to write this equation in 'custom equation' option in curve fitting tool or is there any other way to do it?

Alex Sha on 27 Jul 2019
Hi, where are the values of Z?

#### 1 Comment

Gaurav Nanajkar on 27 Jul 2019
Hi Alex, I saw the details of the equation and according to that this equation is for 'rotationally symmetric polynomial'. As I am using it for 2D curve, in my case Z value will be 0

Catalytic on 27 Jul 2019
C = polyfit( sqrt( x.^2+y.^2) , Z, N)

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Matt J on 28 Jul 2019
It's not that polyfit is better or worse at fitting high order polynomials. It's just that high order polynomials are typically a bad thing to use as a model due to numerical instability.
For example the relationship between a polynomial's roots and its coefficients gets unstable at orders higher than about 20, as illustrated below. Notice the errors just in recovering the roots from the coefficients - I haven't even done any curve fitting yet.
>> p=poly(1:20); r=real(roots(p))
r =
19.9999
19.0013
17.9937
17.0185
15.9597
15.0593
13.9302
13.0627
11.9589
11.0225
9.9912
9.0027
7.9994
7.0001
6.0000
5.0000
4.0000
3.0000
2.0000
1.0000
Gaurav Nanajkar on 28 Jul 2019
ok thanks for the clarification Matt. As you mentioned as its a higher order polynomial I will not use polyfit due to higher perecentage error.
Can you please let me know the way to curve fit it as I am not getting how to use in curve fitting app custom function due to sigma?
Matt J on 29 Jul 2019
As you mentioned as its a higher order polynomial I will not use polyfit due to higher perecentage error.
No, that is not what I said. What I said was "It's not that polyfit is better or worse at fitting high order polynomials. It's just that high order polynomials are typically a bad thing...".
Stop using high order polynomials. Use splines instead.