An exact series expansion for the Dottie number

2023/03/31 by Pain, Jean-Christophe · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.17962

Abstract

In this article, an exact series expansion for the Dottie number (solution of the equation cos(x) = x) is presented. Its derivation consists in combining the Kaplan representation of the Dottie number as a series in odd powers of π, with a series for π^2k+1 (k≥ 1) obtained using the Faà di Bruno formula.

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