Irrationality and transcendence of infinite continued fractions of square roots
Volume 184 / 2018
Acta Arithmetica 184 (2018), 31-36
MSC: Primary 11J72.
DOI: 10.4064/aa170221-21-9
Published online: 14 May 2018
Abstract
We give conditions on a sequence $\{a_n\}_{n=1}^\infty$ of positive integers sufficient to ensure that the number defined by the continued fraction expansion $[0;\sqrt{a_1},\sqrt{a_2},\dots ]$ is either irrational or transcendental.
