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

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).

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

References in corpus (2)

• De seriebus divergentibus
• The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion

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