Fibonacci numbers, Euler's 2-periodic continued fractions and moment sequences

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.

Keywords

Classical Analysis and ODEs, Number Theory, 11B39; 44A60

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/219116

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0902.1404
 http://arxiv.org/abs/0902.1404

Collections

arXiv