# 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.