3
votes
5answers
140 views

Why don't taylor series represent the entire function?

Say, I have a continuos function that is infinitely differentiate on the interval $I$. It can then be written as a taylor series. However, taylor series aren't always completely equal to the function ...
3
votes
0answers
222 views

Taking a Fourier transform of Taylor series

My (naive) question is whether it is possible to take the Fourier transform of a Taylor series? Could one use multiplication with $\delta$ to get the function sampled at the point of expansion and ...
5
votes
1answer
861 views

Why Does Substitution In Taylor Series Work? [closed]

The examples given here for example, show that once you know the form of a taylor polynomial as a function of $x$, you can replace the $x$ with another function. It works when you work out the ...
12
votes
6answers
3k views

Intuition explanation of taylor expansion?

Could you provide a geometric explanation of taylor expansion?
45
votes
4answers
7k views

Connection between Fourier transform and Taylor series

Both Fourier transform and Taylor series are means to represent functions in a different form. My question: What is the connection between these two? Is there a way to get from one to the other (and ...