Exercises in Iterational Asymptotics II
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929744082108416 |
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| author | Finch, Steven |
| author_facet | Finch, Steven |
| contents | The nonlinear recurrences we consider here include the functions $3x(1-x)$ and $\cos(x)$, which possess attractive fixed points $2/3$ and $0.739...$ (Dottie's number). Detailed asymptotics for oscillatory convergence are found, starting with a 1960 paper by Wolfgang Thron. Another function, $x/(1+x\ln(1+x))$, gives rise to a sequence with monotonic convergence to $0$ but requires substantial work to calculate its associated constant $C$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_06065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exercises in Iterational Asymptotics II Finch, Steven Number Theory Discrete Mathematics Classical Analysis and ODEs Combinatorics 39A20 (Primary) 11B37, 26A18, 37E05, 41A60, 65D20 (Secondary) The nonlinear recurrences we consider here include the functions $3x(1-x)$ and $\cos(x)$, which possess attractive fixed points $2/3$ and $0.739...$ (Dottie's number). Detailed asymptotics for oscillatory convergence are found, starting with a 1960 paper by Wolfgang Thron. Another function, $x/(1+x\ln(1+x))$, gives rise to a sequence with monotonic convergence to $0$ but requires substantial work to calculate its associated constant $C$. |
| title | Exercises in Iterational Asymptotics II |
| topic | Number Theory Discrete Mathematics Classical Analysis and ODEs Combinatorics 39A20 (Primary) 11B37, 26A18, 37E05, 41A60, 65D20 (Secondary) |
| url | https://arxiv.org/abs/2501.06065 |