Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers

被引：9
|
作者：
Elsner, Carsten [1 ]
Shimomura, Shun [2 ]
Shiokawa, Iekata [2 ]
机构：
[1] Natl Kaohsiung Univ Appl Sci, FHDW Hannover, D-30173 Hannover, Germany
[2] Keio Univ, Dept Math, Kohoku Ku, Yokohama, Kanagawa 2238522, Japan
来源：
RAMANUJAN JOURNAL | 2008年 / 17卷 / 03期
关键词：
Algebraic independence; Fibonacci numbers; Lucas numbers; Jacobian elliptic functions; Ramanujan functions; q-series; Nesterenko's theorem;
D O I：
10.1007/s11139-007-9019-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove the algebraic independence of the reciprocal sums of odd terms in Fibonacci numbers Sigma(infinity)(n=1) F-2n-1(-1), Sigma(infinity)(n=1) F-2n-1(-2) (n=1), Sigma(infinity)(n=1) F(2n-1)(-3)and write each Sigma(infinity)(n=1) F-2n-1(-s) (s >= 4) as an explicit rational function of these three numbers over Q. Similar results are obtained for various series including the reciprocal sums of odd terms in Lucas numbers.
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页码：429 / 446
页数：18
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