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Explicitly Summing Result of using Sep or Var to solve Laplace's Eqn.

  1. Mar 1, 2013 #1
    1. The problem statement, all variables and given/known data

    for some potential problem, and after using separation of variables

    2. Relevant equations

    V(x,y) = 4V0/∏ Ʃn=1,3,5... 1/n e-n∏x/a sin(n∏y/a) (1)​


    ,where V0 is some specified reference potential and a ε ℝ

    which can be summed explicitly to:

    v(x,y) = 2V0/∏ tan-1(sin(∏y/a)/sinh(∏y/a) (2)​



    3. The attempt at a solution

    I've been out of school for a while, so I don't recall my calculus as best as I should?

    What transform / series would I use for getting from (1) to (2)? No need to spend your time on the gruesome details (leave some fun), but can anyone point me in a general direction?
     
  2. jcsd
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