Arnol'd's limit and the Lagrange inversion

2025/07/30 by Klazar, Martin
#26A03 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #History and Overview (math.HO)

paper · doi:10.48550/arxiv.2507.22743

Abstract

We show how to prove by means of the Lagrange inversion the limit of Arnol'd that lim_x→0(sin(tan x)-tan(sin x))/(\arcsin(\arctan x)-\arctan(\arcsin x))=1 . In fact, we obtain a more general result in terms of formal power series.

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