Arnol'd's limit and the Lagrange inversion
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918107802501120 |
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| author | Klazar, Martin |
| author_facet | Klazar, Martin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arnol'd's limit and the Lagrange inversion Klazar, Martin Classical Analysis and ODEs Combinatorics History and Overview 26A03 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. |
| title | Arnol'd's limit and the Lagrange inversion |
| topic | Classical Analysis and ODEs Combinatorics History and Overview 26A03 |
| url | https://arxiv.org/abs/2507.22743 |