English

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

Number Theory 2022-03-04 v2

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 π\pi in decimal or in binary, it also makes it possible to obtain the nthn^{\rm th} digit of powers of πn\pi^n.

Keywords

Cite

@article{arxiv.2201.12601,
  title  = {A formula for the $n^{\rm th}$ decimal digit or binary of $\pi$ and powers of $\pi$},
  author = {Simon Plouffe},
  journal= {arXiv preprint arXiv:2201.12601},
  year   = {2022}
}

Comments

Added a formula for n! much better than Stirling