For a standard Cauchy distribution f(x)=1π(1+x2)f(x) = \frac{1}{\pi(1+x^2)}f(x)=π(1+x2)1, what is the characteristic function ϕ(t)\phi(t)ϕ(t)?
e−∣t∣e^{-|t|}e−∣t∣
e−t2/2e^{-t^2/2}e−t2/2
1−∣t∣1-|t|1−∣t∣
e−ite^{-it}e−it