Algebraic relations for reciprocal sums of even terms in Fibonacci numbers

Carsten Elsner, Shun Shimomura, Iekata Shiokawa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we discuss the algebraic independence and algebraic relations, first, for reciprocal sums of even terms in Fibonacci numbers, and second, for sums of evenly even and unevenly even types. The numbers, and are shown to be algebraically independent, and each sum is written as an explicit rational function of these three numbers over ℚ. Similar results are obtained for various series of even type, including the reciprocal sums of Lucas numbers, and.

Original languageEnglish
Pages (from-to)650-671
Number of pages22
JournalJournal of Mathematical Sciences
Volume180
Issue number5
DOIs
Publication statusPublished - 2012 Feb

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Rational functions
Lame number
Term
Algebraic Independence
Lucas numbers
Rational function
Series

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistics and Probability

Cite this

Algebraic relations for reciprocal sums of even terms in Fibonacci numbers. / Elsner, Carsten; Shimomura, Shun; Shiokawa, Iekata.

In: Journal of Mathematical Sciences, Vol. 180, No. 5, 02.2012, p. 650-671.

Research output: Contribution to journalArticle

Elsner, Carsten ; Shimomura, Shun ; Shiokawa, Iekata. / Algebraic relations for reciprocal sums of even terms in Fibonacci numbers. In: Journal of Mathematical Sciences. 2012 ; Vol. 180, No. 5. pp. 650-671.
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