La cuadratura gaussiana seg\'un Gauss

TL;DR

This paper provides an abridged Spanish translation and commentary on Gauss's 1815 memoir, revealing his original approach to Gaussian quadrature through series and continued fractions, differing from standard treatments.

Contribution

It offers the first detailed translation and commentary on Gauss's original work, highlighting his unique methods in deriving Gaussian quadrature rules.

Findings

Gauss's original method uses series and continued fractions.

The approach differs from standard textbook treatments.

The memoir exemplifies mathematical virtuosity in functional approximation.

Abstract

This article is an abridged and commented translation into Spanish of the 1815 memoir where Gauss introduced the quadrature rules now associated with his name. Gauss' work does not resemble at all the stardard text-book treatment of Gaussian quadrature. The original memoir is an example of mathematical virtuosity, based on a superb use of series, where the problem is reformulated as a problem in functional approximation that is solved by means of continued fractions.