Iterated Radical Expansions and Convergence

Autor:	Finch, Steven
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Computer Science - Discrete Mathematics Mathematics - Combinatorics 39A20 (Primary) 11B37 26A18 37E05 40A20 65D20 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We treat three recurrences involving square roots, the first of which arises from an infinite simple radical expansion for the Golden mean, whose precise convergence rate was made famous by Richard Bruce Paris in 1987. A never-before-seen proof of an important formula is given. The other recurrences are non-exponential yet equally interesting. Asymptotic series developed for each of these two examples feature a constant, dependent on the initial condition but otherwise intrinsic to the function at hand. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.02114 Zobrazit plný text záznamu View this record from Arxiv