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Transcendence of Certain Reciprocal Sums of Linear Recurrences

✍ Scribed by Daniel Duverney; Tomoaki Kanoko; Taka-aki Tanaka

Publisher
Springer Vienna
Year
2002
Tongue
English
Weight
130 KB
Volume
137
Category
Article
ISSN
0026-9255

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πŸ“œ SIMILAR VOLUMES

Transcendency Results for Sums of Recipr
Transcendency Results for Sums of Reciprocals of Linear Recurrences
✍ 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.

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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