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

English Title

A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers

Authors

Leonhard Euler

Enestrom Number

750

Fuss Index

101

Original Language

Latin

Content Summary

Euler gives a continued fraction representation for (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√-1, for "vanishing" n, and for infinite n.

Published as

Journal article

Published Date

1818

Written Date

1780

Original Source Citation

Mémoires de l'académie des sciences de St.-Petersbourg, Volume 6, pp. 3-11.

Opera Omnia Citation

Series 1, Volume 16B, pp.232-240.

Record Created

2018-09-25