Connection between Fourier transform and Taylor series

[Ganesh Ujwal]

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 back again)? Is there an overall, connceting (geometric?) intuition?

 

[HallsofIvy]

I really am not clear on what your question is. What, exactly do you mean by "connection" here? You ask if possible to go from one to the other but "Fourier transforms" and "Taylors series", to begin with, apply to very different functions. In order to have a "Fourier transform", a function need only be integrable while, in order to have a "Taylors series" a function must be infinitely differentiable, a much more rigorous condition.