A formula for the $n^{\mathrm{th}}$ decimal digit or binary of $\pi$ and powers of $\pi$

Abstract

By using an asymptotic formula known for the numbers of Euler and Bernoulli it is possible to obtain an explicit expression of the nth digit of $\pi$ in decimal or in binary, it also makes it possible to obtain the $n^{\mathrm{th}}$ digit of powers of ${\pi }^n$.

Added a formula for n! much better than Stirling