Observationes generales circa series, quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur

TL;DR

This paper explores the binomial expansion for complex numbers, discusses divergent series sums, and provides translations of Euler's original Latin work into German, contributing to mathematical analysis and historical understanding.

Contribution

It offers insights into Euler's treatment of complex binomial expansions and divergent series, with a translation that enhances accessibility of historical mathematical texts.

Findings

Analysis of binomial series for complex numbers

Euler's methods for divergent series sums

Translation of Euler's Latin work into German

Abstract

This paper, along with E592 and E636, seems to consider the binomial expansion (1+z)^n in the case where z is complex. Euler even gives the sums of divergent series. The paper is translated from Euler's Latin original into German.