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

2022/01/29 by Simon Plouffe, Plouffe, Simon · 2 voices · 3 citations
Mathematics · #Advanced Mathematical Identities #History and Theory of Mathematics #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2201.12601

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 πⁿ.

Cited by

• Bailey–Borwein–Plouffe formula [wikipedia]
• Pi [wikipedia]
• Simon Plouffe [wikipedia]

Discussions

• A formula for the nth digit of 𝜋 and 𝜋^n [hn, 268 points, 133 comments]
• A formula for the n’th digit of 𝜋 and 𝜋^n [bsky, 0 points, 0 comments]

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