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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…
math.NT2019
Linear independence results for certain sums of reciprocals of Fibonacci and Lucas numbers
Daniel Duverney, Yuta Suzuki, Yohei Tachiya
The aim of this paper is to give linear independence results for the values of certain series. As an application, we derive arithmetical properties of the sums of reciprocals of Fi…