POINCARÉ, HENRI (+) FELIX KLEIN.

Sur les Fonctions Uniformes qui se reproduisent par des Substitutions Linéaires (+) [Klein's introduction to the present paper].

Leipzig, B.G. Teubner, 1882. 8vo. Original printed wrappers, no backstrip. In "Mathematische Annalen. Begründet 1882 durch Rudolf Friedrich Alfred Clebsch. XIX. [19] Band. 4. Heft." Entire issue offered. [Poincaré:] Pp. 553-64. [Entire issue: Pp. 435-594].

First printing of Poincaré's paper on his comprehensive theory of complex-valued functions which remain invariant under the infinite, discontinuous group of linear transformations. In 1881 Poincaré had published a few short papers with some initial work on the topic, and in the 1881, Klein invited Poincaré to write a longer exposition of his results to Mathematische Annalen which became the present paper.

This, however, turned out to be an invitation to at mathematical dispute:
"Before the article went to press, Klein forewarned Poincaré that he had appended a note to it in which he registered his objections to the terminology employed therein. In particular, Klein disputed Poincaré's decision to name the important class of functions possessing a natural boundary circle after Fuch's, a leading exponent of the Berlin school. The importance he attached to this matter, however, went far beyond the bounds of conventional priority dispute. True, Klein was concerned that his own work received sufficient acclaim, but the overriding issue hinged on whether the mathematical community would regard the burgeoning research in this field as an outgrowth of Weierstrassian analysis or the Riemannian tradition." Parshall. The Emergence of the American Mathematical Research Community. Pp. 184-5.

The issue contains the following important contributions by seminal mathematicians:
1. Klein, Felix. Ueber eindeutige Functionen mit linearen Transformationen in sich. Pp. 565-68.
2. Picard, Emile. Sur un théorème relatif aux surfaces pour lesquelles les coordnnées d´un point quelconque s´experiment par des fonctions abéliennes de deux paramètres. Pp. 578-87.
3. Cantor, Georg. Ueber ein neues und allgemeines Condensationsprincip der Singularitäten von Functionen. Pp. 588-94.

Order-nr.: 44432