What is the characteristic function of the Cauchy distribution f(x)=1π(1+x2)f(x) = \frac{1}{\pi(1+x^2)}f(x)=π(1+x2)1?
e−∣t∣e^{-|t|}e−∣t∣
e−t2/2e^{-t^2/2}e−t2/2
11+t2\frac{1}{1+t^2}1+t21
e−te^{-t}e−t