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.

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