Fibonacci Numbers and Continued Fraction Expansions [chapter]

Michael Drmota
1993 Applications of Fibonacci Numbers  
In this paper, we provide a method for constructing a continued fraction approximation based on a given asymptotic expansion. We establish some asymptotic expansions for the harmonic numbers which employ the nth triangular number. Based on these expansions, we derive the corresponding continued fraction approximations for the harmonic numbers. * Corresponding author. Chao-Ping Chen 2010 Mathematics Subject Classification. 40A05, 41A20
doi:10.1007/978-94-011-2058-6_17 fatcat:jmarupg5cjfvhmeyg64selj63i