Carl David Tolmé Runge (1856-1927)
- Runge, C., Über die Darstellung
willkürlicher Functionen, Acta Math. 7 (1885/86),
387-392. This paper contains a proof of the fact that any continuous
function on a finite interval can be uniformly approximated by rational
functions. Phragmén (see footnote in Mittag-Leffler's 1900 paper)
pointed out that Runge's previous article (Acta Math. 6)
contains a method of replacing the rational functions by polynomials.
These papers do not explicitly contain Weierstrass' Theorem.