Carl David Tolmé Runge (1856-1927)

• Carl David Tolmé Runge at MacTutor.

• Carl David Tolmé Runge at Wikipedia.

• Carl David Tolmé Runge at the Mathematics Genealogy Project.

• Runge, C., Zur Theorie der eindeutigen analytischen Functionen, Acta Math. 6 (1885), 229-244.

• 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. Review in Jahrbuch Database JFM.

• Runge, C., Über empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten, Zeit. Math. Phys. 46 (1901), 224-243.