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http://dx.doi.org/10.5831/HMJ.2021.43.2.259

FOURIER SERIES OF A DEVIL'S STAIRCASE

Kwon, DoYong (Department of Mathematics, Chonnam National University)

Publication Information

Honam Mathematical Journal / v.43, no.2, 2021 , pp. 259-267 More about this Journal

Abstract

Given 𝛽 > 1, we consider real numbers whose 𝛽-expansions are Sturmian words. When the slope of Sturmian words varies, their behaviors have been well studied from analytical point of view. The regularity enables us to find the Fourier series expansion, while the singularity at rational slopes yields a new kind of trigonometric series representing 𝜋.

Keywords

${\beta}$ -expansion; Sturmian word; Fourier series; singular function; ${\pi}$ ;

Citations & Related Records

Reference

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