Transcendence of reciprocal sums of binary recurrences
β 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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## 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.
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
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