Algebraic relations for reciprocal sums of even terms in Fibonacci numbers

Carsten Elsner, Shun Shimomura, Iekata Shiokawa

Research output: Contribution to journalArticlepeer-review

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 1

ASJC Scopus subject areas

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

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