Math 487, Homework 5

\(\def\Res{\mathtt{Res}}\)

  1. Find function with Laplace transform equal to \[\frac{s^3 – 1}{(1 + s)^4}.\]
  2. Find Fourier coefficients of the function \(t^3-\pi^2 t\) on \([-\pi,\pi]\).
    Use Parseval’s identity to find \[\sum_{n=1}^\infty 1/n^6.\]
  3. Find general formula for the coefficients of the generating function \(W(z)\) given by \(W=1+zW^4\).
  4. Find asymptotic frequency of the numbers \(n\) such that the first digits of \(2^n\) and \(3^n\) coincide.
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