Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit

2012/01/31 by Euler, Leonhard, Diener, Artur, Aycock, Alexander
#FOS: Mathematics #History and Overview (math.HO)

paper · doi:10.48550/arxiv.1202.0035

Abstract

Euler gives a continued fraction representation of (1 + x)n. involving 1,3,5,7,... and n²-1,n²-4,n³-9,... and squares of z, for x=2y and y=z/(1-z). He evaluates this continued fraction at z=t sqrt(-1), for "vanishing" n, and for infinite n and deduces a continued fraction for log, arctan, etc. The paper is translated from Euler's Latin original into German.

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