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arXiv · 1202.0035

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

Leonhard Euler·Artur Diener·Alexander Aycock
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Abstract

Euler gives a continued fraction representation of (1 + x)n. involving 1,3,5,7,... and n^2-1,n^2-4,n^3-9,... 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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Leonhard Euler, Artur Diener, Alexander Aycock. 2012-01-31. Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit. https://arxiv.org/abs/1202.0035

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