A formula for the $n^{\rm th}$ decimal digit or binary of $π$ and powers of $π$
Simon Plouffe
Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.
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 $π$ in decimal or in binary, it also makes it possible to obtain the $n^{\rm th}$ digit of powers of $π^n$.
Linked by 1 identifiable commenter in 1 comment across 1 thread, from May 2022 to May 2022. Found in 1 HN submission from Jan 2023 to Jan 2023. Open submission discussions.
I was very surprised to learn that Plouffe has actually also devised a formula that gives the nth decimal digit! It looks like this was a much more recent discovery. https://mathworld.wolfram.com/Digit-ExtractionAlgorithm.html https://arxiv.org/abs/2201.12601 I first wrote that…
I was very surprised to learn that Plouffe has actually also devised a formula that gives the nth decimal digit! It looks like this was a much more recent discovery. https://mathworld.wolfram.com/Digit-ExtractionAlgorithm.html https://arxiv.org/abs/2201.12601 I first wrote that…
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