4 papers
Algebraic independence of certain infinite products involving the Fibonacci numbers
Daniel Duverney, Yohei Tachiya
Let be the sequence of the Fibonacci numbers. The aim of this paper is to give explicit formulae for the infinite products \[ \prod_{n=1}^{\infty}\left( 1+\fra…
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.
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…
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…