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

TL;DR

This paper discusses the extension of Newton's binomial theorem to fractional exponents, highlighting Euler's recursive relation for binomial coefficients and their power series expansion.

Contribution

It introduces a method to extend Newton's binomial theorem to fractional exponents using Euler's recursive relation.

Findings

Validated the extension of binomial theorem to fractional exponents

Demonstrated the recursive relation for binomial coefficients

Connected power series expansion with Euler's notes

Abstract

Here Euler notes the recursive relation for the general binomial coefficients, by assuming that (1+x)^a can be expanded in a power series.