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Euler's Method of Trigonometric Series- Real Analysis

  1. Feb 6, 2013 #1
    1. The problem statement, all variables and given/known data

    Use Equation (1) to derive the formula: (1-a*cos(phi))/(1-2*a*cos(phi)+a^2))= 1+a*cos(phi)+a^2(cos(2phi))+a^3(cos(3phi))...

    2. Relevant equations

    Equation (1) is 1/(1-a(cos(phi)+isin(phi)))= 1+ [a(cos(phi)+isin(phi)]+ [a(cos(phi)+isin(phi)]^2 + [a(cos(phi)+isin(phi)]^3...

    3. The attempt at a solution

    I know that you are supposed to somehow use that (cos(phi)+isin(phi))^k= cos(kphi)+ isin(kphi), but I'm not sure how to go about this at all. Please help!
  2. jcsd
  3. Feb 6, 2013 #2
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