English Title

A demonstration of a theorem of Newton on the expansion of the powers of a binomial by cases, in which the exponents are not integral numbers

Authors

Leonhard Euler

Enestrom Number

465

Fuss Index

130

Original Language

Latin

Published as

Journal article

Published Date

1775

Written Date

1773

Content Summary

In Institutiones calculi differentialis, Euler showed that (1+x)a = 1 + C(a,1)x + C(a,2)x2 + C(a,3)x3 + .... Here, Euler shows it for arbitrary real values of a and makes use of a functional equation, namely if f(a) = (1+x)a, then f(a)∙f(b) = f(a+b).

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 19, pp. 103-111.

Opera Omnia Citation

Series 1, Volume 15, pp.207-216.

Record Created

2018-09-25

Included in

Mathematics Commons

Share

COinS