Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary

Henri Cohen

Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary

Number Theory 2026-07-03 v1

Authors: Henri Cohen

Abstract

After giving a number of properties of continued fractions of polynomial type, in particular focusing on convergence properties and Bauer-Muir-Ap\'ery 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.

Keywords

continued fractions polynomial type convergence Bauer-Muir-Apéry acceleration special functions encyclopedic dictionary

Cite

@article{arxiv.2607.06581,
  title  = {Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary},
  author = {Henri Cohen},
  journal= {arXiv preprint arXiv:2607.06581},
  year   = {2026}
}

Comments

This is a 664 page book which is the expanded version of the database available in the TeX source of arXiv:2409.06086v4 which should be uploaded so as to have all the continued fractions available in a CAS. Comments, corrections, and especially additions are more than welcome