A simple algorithm for expanding a power series as a continued fraction
Combinatorics
2023-07-03 v2 Classical Analysis and ODEs
Complex Variables
Abstract
I present and discuss an extremely simple algorithm for expanding a formal power series as a continued fraction. This algorithm, which goes back to Euler (1746) and Viscovatov (1805), deserves to be better known. I also discuss the connection of this algorithm with the work of Gauss (1812), Stieltjes (1889), Rogers (1907) and Ramanujan, and a combinatorial interpretation based on the work of Flajolet (1980).
Keywords
Cite
@article{arxiv.2206.15434,
title = {A simple algorithm for expanding a power series as a continued fraction},
author = {Alan D. Sokal},
journal= {arXiv preprint arXiv:2206.15434},
year = {2023}
}
Comments
LaTeX2e, 48 pages. Version 2 contains a few additional historical remarks, and adds a new Remark 4 at the end of Section 10. To be published in Expositiones Mathematicae