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FOURIER SERIES OF A DEVIL'S STAIRCASE

  • Kwon, DoYong (Department of Mathematics, Chonnam National University)
  • Received : 2021.01.22
  • Accepted : 2021.03.25
  • Published : 2021.06.25

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

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B02010219).

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