Sokal, Alan D;
(2022)
A simple algorithm for expanding a power series as a continued fraction.
Expositiones Mathematicae
10.1016/j.exmath.2022.12.001.
(In press).
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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).
| Type: | Article |
|---|---|
| Title: | A simple algorithm for expanding a power series as a continued fraction |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.exmath.2022.12.001 |
| Publisher version: | https://doi.org/10.1016/j.exmath.2022.12.001 |
| Language: | English |
| Additional information: | Copyright © 2022 The Author(s). This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Formal power series, continued fraction, Euler–Viscovatov algorithm, Gauss’s continued fraction, Euler–Gauss recurrence method, Motzkin path, Dyck path, Stieltjes table, Rogers’ addition formula |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10162488 |
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