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

TY - JOUR

T1 - Fibonacci numbers, Euler’s 2-periodic continued fractions and moment sequences

AU - Berg, Christian

AU - Durán, Antonio J.

PY - 2011/2

Y1 - 2011/2

N2 - 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 Fn+1/F n+2, n ≥ 0, of consecutive Fibonacci numbers is a moment sequence.

AB - 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 Fn+1/F n+2, n ≥ 0, of consecutive Fibonacci numbers is a moment sequence.

M3 - Journal article

SN - 0015-0517

VL - 49

SP - 66

EP - 75

JO - Fibonacci Quarterly

JF - Fibonacci Quarterly

ER -