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.

Topics

Infinite Series

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