Irrationality exponents of generalized Hone series
Daniel Duverney, Takeshi Kurosawa, and Iekata Shiokawa
TL;DR
This paper calculates the precise irrationality exponents of specific rational series, extending Hone's earlier work by transforming these series into continued fractions for exact analysis.
Contribution
It introduces a method to determine exact irrationality exponents of generalized Hone series through continued fraction transformations, advancing previous partial results.
Findings
Exact irrationality exponents computed for certain series
Method developed for transforming series into continued fractions
Extends Hone's initial special case to a broader class
Abstract
We compute the exact irrationality exponents of certain series of rational numbers, first studied in a special case by Hone, by transforming them into suitable continued fractions.
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics