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Arnol'd's limit and the Lagrange inversion
Published 30 Jul 2025 in math.CA, math.CO, and math.HO | (2507.22743v1)
Abstract: We show how to prove by means of the Lagrange inversion the limit of Arnol'd that $$ \lim_{x\to0}\frac{\sin(\tan x)-\tan(\sin x)}{\arcsin(\arctan x)-\arctan(\arcsin x)}=1\,. $$ In fact, we obtain a more general result in terms of formal power series.
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