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

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

2012-01-31

arxiv.org/abs/1202.0035v1

Mathematics

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Scientific paper

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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