Weierstrass, K., Über die analytische Darstellbarkeit sogenannter willkürlicher Functionen einer reellen Veränderlichen, Sitzungsberichte der Akademie zu Berlin 633-639 and 789-805, 1885. Weierstrass' paper with his proof of the Weierstrass Theorem on density of algebraic polynomials in the space of continuous real-valued functions on any finite closed interval. Also the analogous result for trigonometric polynomials. An expanded version of this paper with ten additional pages appeared in Weierstrass' "Mathematische Werke", Vol. 3, 1-37, Mayer and Müller, Berlin, 1903.

Weierstrass, K., Sur la possibilité d'une représentation analytique des fonctions dites arbitraires d'une variable réelle, J. Math. Pure et Appl. 2 (1886), 105-113 and 115-138. This is the translation of the Weierstrass 1885 paper and, as the original, it appeared in two parts and in subsequent issues, but under the same title. This journal was, at the time, called Journal de Mathematique or Journal de Liouville.

Pinkus, A., Weierstrass and Approximation Theory, J. Approx. Theory 107 (2000), 1-66. For those with access, this article may also be viewed at Science Direct. Some additions/corrections regarding this paper are in this file. This paper contains some biographical material, but is mainly concerned with the history of the Weierstrass Approximation Theorem. See also the interesting Veselý, J., Weierstrass' theorem before Weierstrass.

Siegmund-Schultze, R., Der Beweis des Weierstrasschen Approximationssatzes 1885 vor dem Hintergrund der Entwicklung der Fourieranalysis (German) [The proof of Weierstrass' approximation theorem of 1885 against the background of the development of Fourier analysis], Historia Math. 15 (1988), 299-310. For those with access, this article may be viewed at Science Direct.