2014/06/06 by Guo-Niu Han, Han, Guo-Niu · 2 citations
Chemistry · Mathematics · #05-04 #05A15 #11A55 #11B50 #11B85 #11C20 #11J82 #11T99 #11Y65 #15-04 #15A15 #15B33 #30B70 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1406.1593
openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hankel determinants of a given power series f can be evaluated by using the Jacobi continued fraction expansion of f. However the existence of the Jacobi continued fraction needs that all Hankel determinants of f are nonzero. We introduce \it Hankel continued fraction, whose existene and unicity are guaranteed without any condition for the power series f. The Hankel determinants can also be evaluated by using the Hankel continued fraction. It is well known that the continued fraction expansion of a quadratic irrational number is ultimately periodic. We prove a similar result for power series. If a power series f over a finite field satisfies a quadratic functional equation, then the Hankel continued fraction is ultimately periodic. As an application, we derive the Hankel determinants of several automatic sequences, in particular, the regular paperfolding sequence. Thus we provide an automatic proof of a result obtained by Guo, Wu and Wen, which was conjectured by Coons-Vrbik.