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math.NT2020
Irrationality exponents of generalized Hone series
Daniel Duverney, Takeshi Kurosawa, Iekata Shiokawa
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.
math.NT2019
Transformation formulas of finite sums into continued fractions
Daniel Duverney, Takeshi Kurosawa, Iekata Shiokawa
We state and prove three general formulas allowing to transform formal finite sums into formal continued fractions and apply them to generalize certain expansions in continued frac…