Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers |
| |
Authors: | C Elsner S Shimomura I Shiokawa |
| |
Institution: | (1) FHDW Hannover, University of Applied Sciences, Freundallee 15, 30173 Hannover, Germany;(2) Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan |
| |
Abstract: | In this paper, we prove the algebraic independence of the reciprocal sums of odd terms in Fibonacci numbers ∑
n=1∞
F
2n−1−1, ∑
n=1∞
F
2n−1−2, ∑
n=1∞
F
2n−1−3 and write each ∑
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.
|
| |
Keywords: | Algebraic independence Fibonacci numbers Lucas numbers Jacobian elliptic functions Ramanujan functions q-series Nesterenko’ s theorem |
本文献已被 SpringerLink 等数据库收录! |
|