Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers

C. Elsner, S. Shimomura, I. Shiokawa

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)429-446
Number of pages18
JournalMolecular Neurodegeneration
Volume3
Issue number1
DOIs
Publication statusPublished - 2008

Keywords

  • Algebraic independence
  • Fibonacci numbers
  • Jacobian elliptic functions
  • Lucas numbers
  • Nesterenko's theorem
  • Q-series
  • Ramanujan functions

ASJC Scopus subject areas

  • Cellular and Molecular Neuroscience
  • Clinical Neurology
  • Molecular Biology

Cite this

Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers. / Elsner, C.; Shimomura, S.; Shiokawa, I.

In: Molecular Neurodegeneration, Vol. 3, No. 1, 2008, p. 429-446.

Research output: Contribution to journalArticle

Elsner, C. ; Shimomura, S. ; Shiokawa, I. / Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers. In: Molecular Neurodegeneration. 2008 ; Vol. 3, No. 1. pp. 429-446.
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