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

Alan D Sokal

doi:10.1016/j.exmath.2022.12.001

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

Alan D Sokal

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https://doi.org/10.1016/j.exmath.2022.12.001

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Journal: Expositiones Mathematicae	Publication Date: Dec 29, 2022
Citations: 1	License type: cc-by

Affiliation: New York University, University College London

#Continued Fraction #Power Series + Show 4 more

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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).

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