Variae considerationes circa series hypergeometricas

TL;DR

This paper discusses Euler's asymptotic approximation for the hypergeometric series and its relation to factorial function interpolation, providing historical insights into Euler's work on transcendent series.

Contribution

It presents a translation of Euler's original Latin work into German, highlighting his approach to asymptotic approximation and factorial interpolation.

Findings

Euler's asymptotic approximation for hypergeometric functions

Recognition of factorial interpolation challenges

Historical translation of Euler's original text

Abstract

Euler gives an asymptotic approximation for the function f(x) and recognizes that he is trying to interpolate the factorial function introduced in E19 "De progressionibus transcendentibus seu quarum termini generales algebraice dari nequeunt". The paper is translated from Euler's Latin original into German.