Hankel continued fraction and its applications

DOI10.1016/j.aim.2016.08.013zbMath1346.05002arXiv1406.1593OpenAlexW2962801931MaRDI QIDQ323670

Guo-Niu Han

Publication date: 10 October 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.1593

zbMATH Keywords

periodicityHankel determinantThue-Morse sequenceautomatic sequenceirrationality exponentautomatic proofHankel continued fractioninteger sequenceregular paperfolding sequencestern sequenceStieltjes algorithm

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Determinants, permanents, traces, other special matrix functions (15A15) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Finite fields and commutative rings (number-theoretic aspects) (11T99) Continued fractions (11A55) Measures of irrationality and of transcendence (11J82) Continued fractions; complex-analytic aspects (30B70) Automata sequences (11B85) Continued fraction calculations (number-theoretic aspects) (11Y65) Software, source code, etc. for problems pertaining to linear algebra (15-04) Sequences (mod (m)) (11B50) Matrices, determinants in number theory (11C20) Software, source code, etc. for problems pertaining to combinatorics (05-04)

Related Items (12)

Stieltjes continued fractions related to the paperfolding sequence and Rudin-Shapiro sequence ⋮ Proof of a conjecture on Hankel determinants for Dyck paths with restricted peak heights ⋮ Hankel continued fractions and Hankel determinants of the Euler numbers ⋮ On the automaticity of sequences defined by the Thue–Morse and period-doubling Stieltjes continued fractions ⋮ On $t$-adic Littlewood conjecture for certain infinite products ⋮ On some conjectures of P. Barry ⋮ Criteria for apwenian sequences ⋮ On Hankel determinants for Dyck paths with peaks avoiding multiple classes of heights ⋮ Jacobi continued fraction and Hankel determinants of the Thue-Morse sequence ⋮ Continued fraction expansions of the generating functions of Bernoulli and related numbers ⋮ On the automaticity of the Hankel determinants of a family of automatic sequences ⋮ Evaluations of certain Catalan-Hankel Pfaffians via classical skew orthogonal polynomials

Cites Work

• A combinatorial proof of the non-vanishing of Hankel determinants of the Thue-Morse sequence
• On the rational approximation to the Thue-Morse-Mahler numbers
• Hankel determinant calculus for the Thue-Morse and related sequences
• Finite automata in number theory
• Combinatorial aspects of continued fractions
• Hankel determinants of the Thue-Morse sequence
• On the rational approximation of the sum of the reciprocals of the Fermat numbers
• Algebraic independence of the generating functions of Stern's sequence and of its twist
• On the irrationality exponent of the regular paperfolding numbers
• Advanced determinant calculus: a complement
• Hankel Determinants, Padé Approximations, and Irrationality Exponents
• On the Stern sequence and its twisted version
• Computer Assisted Proof for Apwenian Sequences
• On Hankel determinants of functions given by their expansions in P-fractions
• Quadratic Irrationals
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