PreprintCC BY 4.0arXiv
Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
Abstract
After giving a number of properties of continued fractions of polynomial type, in particular focusing on convergence properties and Bauer-Muir-Apéry acceleration techniques, we give a large list of continued fractions, both for specific real numbers, and for special functions, some extracted from a number of different sources, but most others being probably new. In addition to providing such a list, one of our main additions is to include the exact speed of convergence of these continued fractions (sometimes only up to a multiplicative constant), which is almost always omitted in the literature.
Related
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BibTeX
@misc{cohen2026continued,
title = {{Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary}},
author = {Henri Cohen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.06581},
eprint = {2607.06581},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.06581},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
AU - Henri Cohen
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2607.06581
UR - https://arxiv.org/abs/2607.06581
AB - After giving a number of properties of continued fractions of polynomial type, in particular focusing on convergence properties and Bauer-Muir-Apéry acceleration techniques, we give a large list of continued fractions, both for specific real numbers, and for special functions, some extracted from a number of different sources, but most others being probably new. In addition to providing such a list, one of our main additions is to include the exact speed of convergence of these continued fractions (sometimes only up to a multiplicative constant), which is almost always omitted in the literature.
ER -