SIN, COS, EXP and LOG of Liouville numbers

2022/02/23 by Taboka Chalebgwa, Chalebgwa, Taboka, Sidney A. Morris +1
Physics and Astronomy · #11J17 #11J91 #Advanced Mathematical Theories and Applications #Experimental and Theoretical Physics Studies #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2202.11293

openalex publication_date 2022/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any Liouville number α, all of the following are transcendental numbers: \textrme^α, log_\textrmeα, sin α, cosα, tanα, \sinhα, \coshα, \tanhα, \arcsinα and the inverse functions evaluated at α of the listed trigonometric and hyperbolic functions, noting that wherever multiple values are involved, every such value is transcendental. This remains true if "Liouville number" is replaced by "U-number", where U is one of Mahler's classes of transcendental numbers.

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