Algebraic relations for reciprocal sums of odd ter

Authors: C Elsner S Shimomura I Shiokawa

Publish Date: 2007/09/18

Volume: 17, Issue: 3, Pages: 429-446

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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

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