Tsukuba Journal of Mathematics

Algebraic independence of modified reciprocal sums of products of Fibonacci numbers

Taka-aki Tanaka

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Abstract

In this paper we establish, using Mahler's method, the algebraic independence of reciprocal sums of products of Fibonacci numbers including slowly increasing factors in their numerators (see Theorems 1, 5, and 6 below). Theorems 1 and 4 are proved by using Theorems 2 and 3 stating key formulas of this paper, which are deduced from the crucial Lemma 2. Theorems 5 and 6 are proved by using different technique. From Theorems 2 and 5 we deduce Corollary 2, the algebraic independence of the sum of a certain series and that of its subseries obtained by taking subscripts in a geometric progression.

Article information

Source
Tsukuba J. Math., Volume 30, Number 2 (2006), 345-361.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496165067

Digital Object Identifier
doi:10.21099/tkbjm/1496165067

Mathematical Reviews number (MathSciNet)
MR2271304

Zentralblatt MATH identifier
1204.11122

Citation

Tanaka, Taka-aki. Algebraic independence of modified reciprocal sums of products of Fibonacci numbers. Tsukuba J. Math. 30 (2006), no. 2, 345--361. doi:10.21099/tkbjm/1496165067. https://projecteuclid.org/euclid.tkbjm/1496165067


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