Algebraic relations with the infinite products generated by Fibonacci numbers

Takeshi Kurosawa, Yohei Tachiya, Takaaki Tanaka

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we establish explicit algebraic relations among infinite products including Fibonacci and Lucas numbers with subscripts in geometric progressions. The algebraic relations given in this paper are obtained by using general criteria for the algebraic dependency of such infinite products.

Original languageEnglish
Pages (from-to)107-119
Number of pages13
JournalAnnales Mathematicae et Informaticae
Volume41
Publication statusPublished - 2013

Fingerprint

Infinite product
Lame number
Subscript
Geometric progression
Lucas numbers

Keywords

  • Algebraic independence
  • Fibonacci numbers
  • Infinite products
  • Mahler functions

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science(all)

Cite this

Algebraic relations with the infinite products generated by Fibonacci numbers. / Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Takaaki.

In: Annales Mathematicae et Informaticae, Vol. 41, 2013, p. 107-119.

Research output: Contribution to journalArticle

@article{1a8ee94dd1294f4e8c371f4ebcedc434,
title = "Algebraic relations with the infinite products generated by Fibonacci numbers",
abstract = "In this paper, we establish explicit algebraic relations among infinite products including Fibonacci and Lucas numbers with subscripts in geometric progressions. The algebraic relations given in this paper are obtained by using general criteria for the algebraic dependency of such infinite products.",
keywords = "Algebraic independence, Fibonacci numbers, Infinite products, Mahler functions",
author = "Takeshi Kurosawa and Yohei Tachiya and Takaaki Tanaka",
year = "2013",
language = "English",
volume = "41",
pages = "107--119",
journal = "Annales Mathematicae et Informaticae",
issn = "1787-5021",
publisher = "Eszterhazy Karoly College",

}

TY - JOUR

T1 - Algebraic relations with the infinite products generated by Fibonacci numbers

AU - Kurosawa, Takeshi

AU - Tachiya, Yohei

AU - Tanaka, Takaaki

PY - 2013

Y1 - 2013

N2 - In this paper, we establish explicit algebraic relations among infinite products including Fibonacci and Lucas numbers with subscripts in geometric progressions. The algebraic relations given in this paper are obtained by using general criteria for the algebraic dependency of such infinite products.

AB - In this paper, we establish explicit algebraic relations among infinite products including Fibonacci and Lucas numbers with subscripts in geometric progressions. The algebraic relations given in this paper are obtained by using general criteria for the algebraic dependency of such infinite products.

KW - Algebraic independence

KW - Fibonacci numbers

KW - Infinite products

KW - Mahler functions

UR - http://www.scopus.com/inward/record.url?scp=84878746918&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878746918&partnerID=8YFLogxK

M3 - Article

VL - 41

SP - 107

EP - 119

JO - Annales Mathematicae et Informaticae

JF - Annales Mathematicae et Informaticae

SN - 1787-5021

ER -