Disquitiones analyticae super evolutione potestatis trinomialis (1+x+xx)^n

TL;DR

Euler explores the Taylor series expansion of (1+x+xx)^n to evaluate integrals, showcasing an analytical approach that predates modern residue calculus methods.

Contribution

The paper provides an early analytical method for integral evaluation using Taylor series, offering insights into polynomial expansions and their applications.

Findings

Derived Taylor series for (1+x+xx)^n

Evaluated integrals using series expansion techniques

Connected series results with integral calculus methods

Abstract

Euler investigates the Taylorseries of (1+x+xx)^n and uses the results to evaluates some integrals which are today often proved with the calculus of residues.