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A simple algorithm for expanding a power series as a continued fraction |
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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). |
| 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 |
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