Register to reply

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

by zetafunction
Tags: divergent, fourier, series, simply, truncate
Share this thread:
zetafunction
#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
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
mathman
#2
Nov11-12, 02:45 PM
Sci Advisor
P: 6,040
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
#3
Nov11-12, 03:06 PM
Engineering
Sci Advisor
HW Helper
Thanks
P: 6,967
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