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Transcendence of reciprocal sums of binary recurrences

✍ Scribed by Tomoaki Kanoko; Takeshi Kurosawa; Iekata Shiokawa


Publisher
Springer Vienna
Year
2008
Tongue
English
Weight
221 KB
Volume
157
Category
Article
ISSN
0026-9255

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πŸ“œ SIMILAR VOLUMES


Transcendency Results for Sums of Recipr
✍ Paul-Georg Becker; Thomas TΓΆpper πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 532 KB

## Abstract Suppose that {__R~n~__}__n__β‰₯0 is a linear recursive sequence and __d__ β‰₯ 2 is an integer. Under suitable conditions on {__R~n~__} and __d__ we show that and similarly constructed numbers are transcendental. Special attention is given to the case of binary recurrences.

Transcendence of certain series involvin
✍ 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

Sums of Factorials in Binary Recurrence
✍ George Grossman; Florian Luca πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 141 KB

In this paper, we consider the problem of expressing a term of a given nondegenerate binary recurrence sequence as a sum of factorials. We show that if one bounds the number of factorials allowed, then there are only finitely many effectively computable terms which can be represented in this way. As