Nova demonstratio, quod evolutio potestatum binomii Newtoniana etiam pro exponentibus fractis valeat

English Title

A new demonstration, with respect to which prevails the expansion of binomial powers by Newton even by fractional exponents

Authors

Leonhard Euler

Enestrom Number

637

Fuss Index

131

Original Language

Latin

Content Summary

Here, Euler notes a recursive relation for the general binomial coefficients. Namely, if (1+x)ⁿ = 1 + Ax + Bx² + Cx³ + Dx⁴ + ... and (1+x)ⁿ⁺¹ = 1 + A'x + B'x² + C'x³ + D'x⁴ + ..., then A' = A+1, B' = B+A, C' = C+B, D' = D+C, etc. This generalizes the usual recursive relationship for the binomial coefficients.

Published as

Journal article

Published Date

1789

Written Date

1776

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 5, pp. 52-58.

Opera Omnia Citation

Series 1, Volume 16A, pp.112-121.

Record Created

2018-09-25