# Example for Lévy's continuity theorem

I am searching a sequence of RV $$(X_n)$$ for which we prove a convergence in distribution to a random variable $$X$$, using the fact that the characteristic functions $$(\varphi_n)_n$$ converges pointwise to some function $$\varphi$$ which is continuous at $$0$$, with $$\varphi$$ not the characteristic function of a well-know law (Binomial, Cauchy, Normal, etc).

Thanks