Transforming from Maclaurin to Taylor
4 views (last 30 days)
Show older comments
I have a polynomial function in terms of x, in which the highest power never exceeds 6. This function will look like a Maclaurin Series with finite terms. How to tell Matlab to rewrite this function into a Taylor one, which will express the function in terms of (x-a), where a is a real, positive number?
E.g. Original function: f(x)=x^3+x^2+x+1
Transformed functions:
If a=1, g(x)=(x-1)^3+4*(x-1)^2+6*(x-1)+4
if a=2, g(x)=(x-2)^3+7*(x-2)^2+17*(x-2)+15
and etc.
I tried using rem but it returned an error message, saying that f(x) must be a real value in order to use rem.
0 Comments
Accepted Answer
William Alberg
on 15 May 2020
If i understand correctly, your code looks something like this:
syms x
f(x) = x^3 + x^2 + x +1
f(x-1)
f(x-2)
And you want to expand the expressions. This can be done with the expand command:
expand(f(x-1))
>> x^3 - 2*x^2 + 2*x
expand(f(x-2))
>> x^3 - 5*x^2 + 9*x - 5
3 Comments
William Alberg
on 15 May 2020
Ahh, I completely misunderstood that!
I dont know how to achieve that, since matlab dont like the "k*(x-a)^1" part, and will rewrite it. I can however get the correct "k*(x-a)^n" for n > 1
My (not complete) solution is this:
f(x) = x^3 + x^2 + x +1;
a = 1;
temp = expand(subs(f(x),x,y + a))
g(x) = subs(temp,y,x-a)
>>6*x + 4*(x - 1)^2 + (x - 1)^3 - 2
More Answers (0)
See Also
Categories
Find more on Matrix Indexing in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!