Answer to a question concerning Euler's paper "Variae considerationes circa series hypergeometricas"

TL;DR

This paper addresses a specific problem related to Euler's work on hypergeometric series, providing a solution using methods Euler himself employed, thus deepening understanding of Euler's original mathematical techniques.

Contribution

It offers a solution to a problem posed by Euler's paper on hypergeometric series, applying Euler's methods to modern mathematical analysis.

Findings

Solved a problem concerning Euler's hypergeometric series

Applied Euler's original methods to contemporary problems

Enhanced understanding of Euler's techniques in hypergeometric series

Abstract

We solve a problem concerning Euler's paper "Variae considerationes circa series hypergeometricas" (\cite{E661}) suggested by G. Faber in the preface to Volume 16,2 of the first series of Euler's Opera Omnia by methods proven by Euler on another occasion.