Infinite products related to generalized Thue–Morse sequences

Li, Yao-Qiang

doi:10.1007/s00605-020-01480-x

Cited by 3 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is a rich history associated with the study of the closed-form evaluation of infinite products with automatic sequences involved as exponents. In this regard, references as in [5,6,9,11,20] are relevant to our work and have inspired much about the new results introduced in Section 2 below.…”

Section: Introductionmentioning

confidence: 99%

Infinite products involving the period-doubling sequence

Campbell

2023

Monatsh Math

View full text Add to dashboard Cite

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

show abstract

Section: Introductionmentioning

confidence: 99%

Infinite products involving the period-doubling sequence

Campbell

2023

Monatsh Math

View full text Add to dashboard Cite

show abstract

Automatic sequences and the Glaisher–Kinkelin constant

Campbell

2024

Advances in Applied Mathematics

View full text Add to dashboard Cite

Generalized Koch Curves and Thue–morse Sequences

2021

Fractals

View full text Add to dashboard Cite

Let [Formula: see text] be the well-known [Formula: see text] Thue–Morse sequence [Formula: see text] Since the 1982–1983 work of Coquet and Dekking, it is known that [Formula: see text] is strongly related to the famous Koch curve. As a natural generalization, for [Formula: see text], we use [Formula: see text] to define the generalized Koch curve, where [Formula: see text] is the generalized Thue–Morse sequence defined to be the unique fixed point of the morphism [Formula: see text] [Formula: see text] beginning with [Formula: see text] and [Formula: see text], and we prove that generalized Koch curves are the attractors of the corresponding iterated function systems. For the case that [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the open set condition holds, and then the corresponding generalized Koch curve has Hausdorff, packing and box dimension [Formula: see text], where taking [Formula: see text] and then [Formula: see text] will recover the result on the classical Koch curve.

show abstract

Infinite products related to generalized Thue–Morse sequences

Cited by 3 publications

References 13 publications

Infinite products involving the period-doubling sequence

Infinite products involving the period-doubling sequence

Automatic sequences and the Glaisher–Kinkelin constant

Generalized Koch Curves and Thue–morse Sequences

Contact Info

Product

Resources

About