arXiv Open Access 2012

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

Leonhard Euler Artur Diener Alexander Aycock

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Abstrak

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.

Topik & Kata Kunci

math.HO

Penulis (3)

Leonhard Euler

Artur Diener

Alexander Aycock

Format Sitasi

APA MLA BibTeX

Euler, L., Diener, A., Aycock, A. (2012). Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit. https://arxiv.org/abs/1202.0035

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2012
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓