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. Review in Jahrbuch Database JFM.

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