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Iterated Radical Expansions and Convergence

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arxiv 2410.02114 v2 pith:SBOQ74UH submitted 2024-10-03 math.NT cs.DMmath.CO

Steven Finch This is my paper · ORCID
classification math.NTcs.DMmath.CO
keywords convergenceradicalrecurrencesarisesasymptoticbruceconditionconstant
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Popa's "Recurrent Sequences" and Reciprocity

    math.CA 2024-12 conditional novelty 5.0 of 10

    For a family of nonlinear recurrences, the paper evaluates the asymptotic constant C to 25 digits using a reciprocal transformation and the Mavecha-Laohakosol algorithm.

  2. Exercises in Iterational Asymptotics

    math.NT 2024-11 conditional novelty 5.0 of 10

    For three families of nonlinear recurrences, the paper gives asymptotic expansions and high-precision numerical constants, including a new reciprocity relation for the q=3/2 case.

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