can we simply truncate a Fourier series if it is divergent??


by zetafunction
Tags: divergent, fourier, series, simply, truncate
zetafunction
zetafunction is offline
#1
Nov10-12, 04:04 PM
P: 399
given a Fourier series of the form

[tex] \sum_{n=0}^{\infty}\frac{cos(nx)}{\sqrt{n}}[/tex]

can i simply truncate this series up to some number finite N so i can get finite results ?? thanks.
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
mathman
mathman is offline
#2
Nov11-12, 02:45 PM
Sci Advisor
P: 5,942
You can always truncate the series to get a finite result. However the result as a function of N does not converge to anything.
AlephZero
AlephZero is online now
#3
Nov11-12, 03:06 PM
Engineering
Sci Advisor
HW Helper
Thanks
P: 6,380
Maybe a more fundamental question is "what is your series supposed to represent?" For eaxmple, the energy (measured as the function squared) is ##\sum (1/n)## which is infinite.

As mathman said, you can do anything you like mathematically with a finite number of terms, but whether the result means anything is another question.


Register to reply

Related Discussions
Big O taylor series truncate Calculus & Beyond Homework 4
Divergent series... Calculus 1
Divergent Harmonic Series, Convergent P-Series (Cauchy sequences) Calculus & Beyond Homework 1
divergent series Calculus & Beyond Homework 4