POINCARÉ, HENRI.

Sur les Groupes des Equations linèaires.

(Stockholm, F.& G. Beier), 1885. 4to. Orig. printed wrappers (to Acta Mathematica 4:3). Extracted from "Acta Mathematica", Vol. 4. Pp. 201-312. Clean and fine.

First appearance of a major paper on differential equations of the first order
"...the whole theory of automorphic functions was from the start guided by the idea of integrating linear differential equations with algebraic coefficients. Poincaré simultaneously investigated the local problem of linear differential equation in the neighborhood of an "irregular" singular point, showing for the first time how asymptotic developments could be obtained for the integrals. A little later (1884, the paper offered) he took up the question, also started by I.L. Fuchs, of the determination of all differential equations of the first order (in the complex domain) algebraic in y and y' and having fixed singular points; his rechearches was to be extended by Picard for equations of the second order, and to lead to the spectacular results of Painlevé and his school at the beginning of the tweentieth century."(DSB).

Order-nr.: 41900