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arXiv · 0902.1404

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

Christian Berg·Antonio J. Durán
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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.

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Christian Berg, Antonio J. Durán. 2009-02-09. Fibonacci numbers, Euler's 2-periodic continued fractions and moment sequences. https://arxiv.org/abs/0902.1404

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