Article ID: CBB001252138

The Mittag-Leffler Theorem: The Origin, Evolution, and Reception of a Mathematical Result, 1876--1884 (2013)

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The Swedish mathematician Gösta Mittag-Leffler (1846--1927) is well-known for founding Acta Mathematica, often touted as the first international journal of mathematics. A post-doctoral student in Paris and Berlin between 1873 and 1876, Mittag-Leffler built on Karl Weierstrass' work by proving the Mittag-Leffler Theorem, which states that a function of rational character (i.e. a meromorphic function) is specified by its poles, their multiplicities, and the coefficients in the principal part of its Laurent expansion. In this paper I explore the evolution of the Mittag-Leffler Theorem, from its initial state in 1876 to its final version, published in 1884. Mittag-Leffler's work contributed significantly to Weierstrass' program on the foundations of analysis. His interest in generalizing his results to functions having arbitrarily many essential singularities, however, which led to his research on infinite sets of singular points, attracted him to Georg Cantor's set-theoretic work. As we shall see, his use of Cantor's theorems and definitions was closely linked to his research efforts in the context of Weierstrass' program.

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Description On the Swedish mathematician Gösta Mittag-Leffler (1846--1927).


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Authors & Contributors
Grattan-Guinness, Ivor
Ferreirós, José
Laugwitz, Detlef
Moore, Matthew E.
Mittag-Leffler, Gösta
Poincaré, Henri
Journals
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Historia Mathematica
NTM: Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin
Synthese
Science in Context
Archive for History of Exact Sciences
Publishers
Princeton University Press
Birkhäuser
Les Belles Lettres
Crítica
Franz Steiner Verlag
P. Lang
Concepts
Mathematics
Set theory
Infinity
Infinitesimals
Logic
Collected correspondence
People
Cantor, Georg Ferdinand Ludwig
Mittag-Leffler, Gösta
Dedekind, Richard
Russell, Bertrand Arthur William
Gödel, Kurt
Du Bois-Reymond, Emil Heinrich
Time Periods
19th century
20th century, early
Medieval
20th century
18th century
17th century
Places
Germany
Sweden
Europe
Stockholm
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