How would you use Parseval’s theorem to show that
$$\int_{0}^{\infty} \frac{1}{(k^2+1)^2}=\frac\pi4$$
2026-02-23 02:53:44.1771815224
Use of Parseval’s theorem for deduction
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Hint Find a function $f : [-\pi, \pi] \to \mathbb R$ such that $a_k=\frac{1}{k^2+1}$ and apply Parseval Identiy.