Fibonacci numbers, Euler's 2-periodic continued fractions and moment sequences
Classical Analysis and ODEs
2009-02-10 v1 Number Theory
Abstract
We prove that certain sequences of finite continued fractions associated with a 2-periodic continued fraction with period a,b>0 are moment sequences of discrete signed measures supported in the interval [-1,1], and we give necessary and sufficient conditions in order that these measures are positive. For a=b=1 this proves that the sequence of ratios F_{n+1}/F_{n+2}, n\ge 0 of consecutive Fibonacci numbers is a moment sequence.
Cite
@article{arxiv.0902.1404,
title = {Fibonacci numbers, Euler's 2-periodic continued fractions and moment sequences},
author = {Christian Berg and Antonio J. Durán},
journal= {arXiv preprint arXiv:0902.1404},
year = {2009}
}