‎"MOORE, ELIAKIM HASTINGS.‎
‎Concerning Transcendentally Transcendental Functions.‎

‎Leipzig, B.G. Teubner, 1896. 8vo. In ""Mathematische Annalen, 48. Band, 1-2 Heft, 1896"". In the original printed wrappers, without backstrips. Wrappers with a few nicks and some brownspotting to front wrapper and title page. Library stamp to verso of title page. [Moore:] Pp. 49-74. [Entire issue: IV, 240 pp. + 1 folded plate].‎

Reference : 45061

‎First printing of Moore probe of the theory of functions produced a clarified treatment of transcendentally transcendental functions.""Rigor and generalization characterized the mathe-matical research of Moore. His research fell principally into the areas of (1) geometry" (2) algebra, groups, and number theory (3) the theory of functions" and (4) integral equations and general analysis. Among these he emphasized the second and fourth areas. In geometry he examined the postulational foundations of Hilbert, as well as the earlier works of Pasch and Peano. He skillfully analyzed the independence of the axioms of Hilbert and formulated a system of axioms for n-dimensional geometry, using points only as undefined elements instead of the points, lines, and planes of Hilbert in the three-dimensional case. During his investigation of the theory of abstract groups, he stated and proved for the first time the important theorem that every finite field is a Galois field (1893). He also discovered that every finite group G of linear transformations on n variables has a Hermitian invariant (1896-1898). His probe of the theory of functions produced a clarified treatment of transcendentally transcendental functions and a proof of Goursat’s extension of the Cauchy integral theorem for a function without the assumption of the continuity of the derivative."" (DSB).‎