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

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dc.creatorBerg, Christian
dc.creatorDurán, Antonio J.
dc.date2009-02-09
dc.date.accessioned2026-07-07T12:39:27Z
dc.date.available2026-07-07T12:39:27Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0902.1404
dc.identifierhttp://arxiv.org/abs/0902.1404
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219116
dc.subjectClassical Analysis and ODEs
dc.subjectNumber Theory
dc.subject11B39; 44A60
dc.titleFibonacci numbers, Euler's 2-periodic continued fractions and moment sequences
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