𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Transcendence of certain infinite products

✍ Scribed by Yohei Tachiya

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
204 KB
Volume
125
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

We prove the transcendence results for the infinite product

, where E k (x), F k (x) are polynomials, α is an algebraic number, and r 2 is an integer. As applications, we give necessary and sufficient conditions for transcendence of ∞ k=0 (1

), where F n and L n are Fibonacci numbers and Lucas numbers respectively, and {a k } k 0 is a sequence of algebraic numbers with log a k = o(r k ).

πŸ“œ SIMILAR VOLUMES

On the transcendence of certain series
On the transcendence of certain series
✍ Christopher F Woodcock; Habib Sharif πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 281 KB
A Theorem on Transcendence of Infinite S
A Theorem on Transcendence of Infinite Series II
✍ M.A. Nyblom πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 149 KB

As an application of Roth's theorem concerning the rational approximation of algebraic numbers, a sufficiency condition is derived for a series of positive rational terms to converge to a transcendental number. This condition is then used to obtain similar sufficiency conditions that exist within th

Transcendence of certain series involvin
Transcendence of certain series involving binary linear recurrences
✍ Takeshi Kurosawa πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 228 KB

Duverney and Nishioka [D. Duverney, Ku. Nishioka, An inductive method for proving the transcendence of certain series, Acta Arith. 110 (4) (2003) 305-330] studied the transcendence of k 0 , where E k (z), F k (z) are polynomials, Ξ± is an algebraic number, and r is an integer greater than 1, using a