Recent content by polpol

  1. P

    Convolution proof where f=g=1/(1+x^2)

    Yes that is true, I did a terrible job of writing that out. My main effort has been evaluating the integral on the left hand side because I believe if I can solve for that or show it equal to the right in some way that is all I need.
  2. P

    Convolution proof where f=g=1/(1+x^2)

    You are right; I meant to use the * as multiplication on the right side and that was unclear. I will edit it and fix it.
  3. P

    Convolution proof where f=g=1/(1+x^2)

    One thing I thought was promising was a polynomial integration with \int_{-\infty}^\infty \frac{1}{t^4 +c_1t^3+c_2t^2+c_3t+c_4} dt where c1 = -2x, c2 = 2x^2, c3 = -x, c4 = x^2 + 1 but I couldn't find anything useful from there. I'm interested in seeing this what would your strategies...
  4. P

    Convolution proof where f=g=1/(1+x^2)

    So I am looking for some insight one how I might go about solving this problem. I have two equations f and g where f = g = \frac{1}{(1+x^2)}. The convolution theorem states that L(f*g) = L(f)*L(g) where L can be either the Laplace transform or the Fourier transform. So it will look like this...
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