Algebraic independence of reciprocal sums of certain Fibonacci-type numbers

2014/03/21 by Peter Bundschuh, Bundschuh, Peter, Keijo Väänänen +1
Mathematics · Physics and Astronomy · #11J81 #11J91(Primary) #39B32(Secondary) #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11J81

paper · pdf · doi:10.48550/arxiv.1403.5510

16 pages

arxiv created 2014/03/21 · openalex publication_date 2014/03/21 · arxiv updated 2014/03/24 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The paper studies algebraic independence of certain reciprocal sums of Fibonacci and Lucas sequences. Also more general binary recurrences are considered. The main tool is Mahler's method reducing the investigation of the algebraic independence of function values to the one of functions if these satisfy certain types of functional equations.

Related

• Linear independence results for certain sums of reciprocals of Fibonacci and Lucas numbers
• Algebraic independence of certain Mahler numbers
• Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials
• Fibonacci sums and divisibility properties
• Sums of Reciprocals of Recurrence Relations