2015/03/30 by Geremías Polanco E, E, Geremías Polanco
Computer Science · Mathematics · #11B75 #11B85 (Primary) #11N64 (Secondary) #40A05 #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.CO #math.NT #msc:11B75 #msc:11B85 #msc:11N64 #msc:40A05 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1503.08512
26 pages including bibliography
arxiv created 2015/03/30 · openalex publication_date 2015/03/30 · arxiv updated 2015/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we find an identity that gives a representation for the logarithm of any two irrational numbers a, b >1 in terms of a series whose terms are ratios of elements from the Beatty Sequences generated by these two numbers. We also show that Sturmian sequences can be defined in terms of these ratios. Furthermore, we find an identity for such series that bears a superficial resemblance to (a discrete version of) Frullani's Integral.