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Mathematics > Number Theory

arXiv:2201.12601 (math)
[Submitted on 29 Jan 2022 (v1), last revised 3 Mar 2022 (this
version, v2)]

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

Authors:Simon Plouffe
Download PDF

    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 $n^{\rm th}$ digit of powers
    of $\pi^n$.

Comments:    Added a formula for n! much better than Stirling
Subjects:    Number Theory (math.NT)
MSC classes: 11Y60
Cite as:     arXiv:2201.12601 [math.NT]
             (or arXiv:2201.12601v2 [math.NT] for this version)
             https://doi.org/10.48550/arXiv.2201.12601
             Focus to learn more
             arXiv-issued DOI via DataCite

Submission history

From: Simon Plouffe [view email]
[v1] Sat, 29 Jan 2022 15:06:35 UTC (100 KB)
[v2] Thu, 3 Mar 2022 02:59:50 UTC (101 KB)
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