Vol. 8, No. 1, 2019

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Transcendence of numbers related with Cahen's constant

Daniel Duverney, Takeshi Kurosawa and Iekata Shiokawa

Vol. 8 (2019), No. 1, 57–69
DOI: 10.2140/moscow.2019.8.57

Cahen’s constant is defined by the alternating sum of reciprocals of terms of Sylvester’s sequence minus 1. Davison and Shallit proved the transcendence of the constant and Becker improved it. In this paper, we study rationality of functions satisfying certain functional equations and generalize the result of Becker by a variant of Mahler’s method.

Cahen's constant, transcendence, Mahler's method, Sylvester's sequence
Mathematical Subject Classification 2010
Primary: 11J81
Received: 10 January 2018
Accepted: 14 March 2018
Published: 11 August 2018
Daniel Duverney
Baggio Engineering School
Takeshi Kurosawa
Department of Applied Mathematics
Tokyo University of Science
Iekata Shiokawa
Department of Mathematics
Keio University