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!

Solving for variable inside summations

  1. May 24, 2012 #1
    Hi,

    I have an equation:

    [itex]\frac{q-\bar{q}}{w_{i}^{2}+w'_{j}^2}=\sum^{n}_{i=0}\sum^{m}_{j=1}F_{0}\cdot a_{ij}\cdot cos(w_{i}\cdot x)\cdot cos(w'_{j}\cdot y)[/itex]

    I'm trying to solve for [itex]a_{ij}[/itex]

    I have the solution, but I'm not sure how they came up with it. The solution is:

    [itex]a_{ij}=\frac{\int^{s}_{0}\int^{w/2}_{0}q-\bar{q}/F_{0}\cdot cos(w_{i}\cdot x)\cdot cos(w'_{j}\cdot y)\cdot dy\cdot dx}{(w_{i}^{2}+w'_{j}^2)\cdot s \cdot w/8}[/itex]


    Any help would be appreciated. Even if it's just a small push in the right direction.

    Cheers
     
  2. jcsd
  3. May 24, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    They are using the fact that, if [itex]\{v_i\}[/itex] is an orthonormal basis for an inner product space and [itex]v= \sum a_iv_i[/itex], then [itex]a_i= <v_i, v>[/itex] where < , > is the inner product.
     
  4. May 30, 2012 #3
    I'll have to read up on that.. thanks a bunch!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving for variable inside summations
Loading...