1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sum derivation

  1. Nov 17, 2009 #1
    suppose, [tex] s_{n}(f;t) = \sum_{k=-n}^{n}\widehat{f}(k)e^{ikt}[/tex]
    and
    [tex]\sigma_{N}(f;t)= \frac{1}{N+1}\sum_{n=0}^{N}s_{n}(f;t)[/tex].

    how do i get from this [tex]\sigma_{N}(f;t)= \frac{1}{N+1}\sum_{n=0}^{N}s_{n}(f;t)[/tex].

    to this


    [tex]\sigma_{N}(f;t)= \sum_{n=-N}^{N}(1-\frac{|n|}{N+1})\widehat{f}(n)e^{int}[/tex]

    obviously one starts with:

    [tex]\sigma_{N}(f;t)=\frac{1}{N+1}\sum_{n=0}^{N}\sum_{k=-n}^{n}\widehat{f}(k)e^{ikt}[/tex]

    thanks!
     
  2. jcsd
  3. Nov 17, 2009 #2
    And what happens when you reverse the order of summation ... the sum on k outside, the sum on n inside?
     
  4. Nov 17, 2009 #3
    ?














    ?
     
  5. Nov 17, 2009 #4
    wow this must be slowest forum on the face of the planet
     
  6. Nov 17, 2009 #5

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    Counterexample: http://www.myfinanceforum.com/
     
  7. Nov 17, 2009 #6
    Perhaps, but remember we're not all free to check forums 25 hours a day, 8 days a week. Two hours 40 for what looks like a hint seems pretty good to me. Have you tried it?
     
  8. Nov 18, 2009 #7
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Sum derivation
  1. Derivative of sum (Replies: 10)

Loading...