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.
"Transcendence of numbers related with Cahen's constant." Mosc. J. Comb. Number Theory 8 (1) 57 - 69, 2019. https://doi.org/10.2140/moscow.2019.8.57