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December 2006 Algebraic independence of modified reciprocal sums of products of Fibonacci numbers
Taka-aki Tanaka
Tsukuba J. Math. 30(2): 345-361 (December 2006). DOI: 10.21099/tkbjm/1496165067

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.

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Taka-aki Tanaka. "Algebraic independence of modified reciprocal sums of products of Fibonacci numbers." Tsukuba J. Math. 30 (2) 345 - 361, December 2006. https://doi.org/10.21099/tkbjm/1496165067

Information

Published: December 2006
First available in Project Euclid: 30 May 2017

zbMATH: 1204.11122
MathSciNet: MR2271304
Digital Object Identifier: 10.21099/tkbjm/1496165067

Rights: Copyright © 2006 University of Tsukuba, Institute of Mathematics

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Vol.30 • No. 2 • December 2006
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