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arXiv:2206.15434 [math.CO]AbstractReferencesReviewsResources

A simple algorithm for expanding a power series as a continued fraction

Alan D. Sokal

Published 2022-06-30Version 1

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).

Comments: LaTeX2e, 47 pages
Categories: math.CO, math.CA, math.CV
Subjects: 30B70, 05A10, 05A15, 05A19
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