2024/11/03 by Steven Finch, Finch, Steven · 1 citation
Mathematics · #26A18 #37E05 #39A20 (Primary) 11B37 #41A60 #65D20 (Secondary) #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Functional Equations Stability Results #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2411.01591
openalex publication_date 2024/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
N. G. de Bruijn (1958) studied the asymptotic expansion of iterates of sin(x) with 0 < x ≤ π/2. Bencherif & Robin (1994) generalized this result to increasing analytic functions f(x) with an attractive fixed point at 0 and x > 0 suitably small. Mavecha & Laohakosol (2013) formulated an algorithm for explicitly deriving required parameters. We review their method, testing it initally on the logistic function ℓ(x), a certain radical function r(x), and later on several transcendental functions. Along the way, we show how ℓ(x) and r(x) are kindred functions; the same is also true for sin(x) and arcsinh(x).