I'm struggling to find a way to integrate $\Phi^n(a_nx + b)$ (I have values for $a_n$ and $b_n$)
I have got $(\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{a_nx+b} \exp(-\frac{y^2}{2}) dy)^n$ but I am unsure on how to proceed.
Eventually I would need to show that this integral tends to $exp(-exp(-x))$ as $n \to \infty$. Any help would be greatly appreciated!
(Apologies for the poor format, I've not used MathJax before)