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
Enestrom Number
465
Fuss Index
130
Original Language
Latin
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).
Published as
Journal article
Published Date
1775
Written Date
1773
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
E465de.pdf (118 kB)
