De termino generali serierum hypergeometricarum

TL;DR

This paper explores Euler's definition of a hypergeometric series function as an infinite product, deriving recursive relationships and asymptotic properties, providing historical insight into early special function theory.

Contribution

It presents a translation and analysis of Euler's original work on hypergeometric series, highlighting his methods and recursive formulas for the function.

Findings

Euler's recursive relationships for the hypergeometric function

Asymptotic analysis of the infinite product representation

Historical translation of Euler's original work

Abstract

Euler defines a function f(x) somehow as an infinite product and a generalization of [x], where [x] ist, what we now call following Legendre the Gamma-Funktion. He gets some recursive relationships for f(x), by applying some very nice tricks and using the asymptotics of the infinite products. The paper is translated from Latin into German.